Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, J

Percentage Accurate: 79.6% → 93.6%

Time: 15.5s

Alternatives: 19

Speedup: 0.7×

• 37.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Initial Program: 79.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Alternative 1: 93.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-35} \lor \neg \left(z \leq 1.3 \cdot 10^{+79}\right):\\ \;\;\;\;\frac{\left(\frac{b}{z} + 9 \cdot \left(\frac{y}{z} \cdot x\right)\right) - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1e-35) (not (<= z 1.3e+79)))
   (/ (- (+ (/ b z) (* 9.0 (* (/ y z) x))) (* 4.0 (* a t))) c)
   (/ (+ b (fma x (* 9.0 y) (* t (* a (* z -4.0))))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1e-35) || !(z <= 1.3e+79)) {
		tmp = (((b / z) + (9.0 * ((y / z) * x))) - (4.0 * (a * t))) / c;
	} else {
		tmp = (b + fma(x, (9.0 * y), (t * (a * (z * -4.0))))) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1e-35) || !(z <= 1.3e+79))
		tmp = Float64(Float64(Float64(Float64(b / z) + Float64(9.0 * Float64(Float64(y / z) * x))) - Float64(4.0 * Float64(a * t))) / c);
	else
		tmp = Float64(Float64(b + fma(x, Float64(9.0 * y), Float64(t * Float64(a * Float64(z * -4.0))))) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1e-35], N[Not[LessEqual[z, 1.3e+79]], $MachinePrecision]], N[(N[(N[(N[(b / z), $MachinePrecision] + N[(9.0 * N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + N[(t * N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.00000000000000001e-35 or 1.30000000000000007e79 < z

   1. Initial program 63.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 63.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 63.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 59.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 59.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 59.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 59.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 65.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 65.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 65.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 78.9%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   6. Taylor expanded in c around 0 87.3%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]
   7. Step-by-step derivation

      1. associate-*r/ 96.2%

         \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(x \cdot \frac{y}{z}\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

      2. *-commutative 96.2%

         \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

   8. Applied egg-rr 96.2%

      \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

   if -1.00000000000000001e-35 < z < 1.30000000000000007e79

   1. Initial program 93.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 93.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 93.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 94.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 94.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 94.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 95.4%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-35} \lor \neg \left(z \leq 1.3 \cdot 10^{+79}\right):\\ \;\;\;\;\frac{\left(\frac{b}{z} + 9 \cdot \left(\frac{y}{z} \cdot x\right)\right) - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 55.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(9 \cdot x\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+121}:\\ \;\;\;\;x \cdot \frac{\frac{y}{c}}{\frac{z}{9}}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-233}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-299}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b}}\\ \mathbf{elif}\;t\_1 \leq 10^{+94}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x \cdot \frac{y}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* 9.0 x))))
   (if (<= t_1 -2e+121)
     (* x (/ (/ y c) (/ z 9.0)))
     (if (<= t_1 -5e-233)
       (* a (/ (* t -4.0) c))
       (if (<= t_1 4e-299)
         (/ 1.0 (/ (* z c) b))
         (if (<= t_1 1e+94)
           (* t (/ (* a -4.0) c))
           (* 9.0 (/ (* x (/ y c)) z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (9.0 * x);
	double tmp;
	if (t_1 <= -2e+121) {
		tmp = x * ((y / c) / (z / 9.0));
	} else if (t_1 <= -5e-233) {
		tmp = a * ((t * -4.0) / c);
	} else if (t_1 <= 4e-299) {
		tmp = 1.0 / ((z * c) / b);
	} else if (t_1 <= 1e+94) {
		tmp = t * ((a * -4.0) / c);
	} else {
		tmp = 9.0 * ((x * (y / c)) / z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (9.0d0 * x)
    if (t_1 <= (-2d+121)) then
        tmp = x * ((y / c) / (z / 9.0d0))
    else if (t_1 <= (-5d-233)) then
        tmp = a * ((t * (-4.0d0)) / c)
    else if (t_1 <= 4d-299) then
        tmp = 1.0d0 / ((z * c) / b)
    else if (t_1 <= 1d+94) then
        tmp = t * ((a * (-4.0d0)) / c)
    else
        tmp = 9.0d0 * ((x * (y / c)) / z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (9.0 * x);
	double tmp;
	if (t_1 <= -2e+121) {
		tmp = x * ((y / c) / (z / 9.0));
	} else if (t_1 <= -5e-233) {
		tmp = a * ((t * -4.0) / c);
	} else if (t_1 <= 4e-299) {
		tmp = 1.0 / ((z * c) / b);
	} else if (t_1 <= 1e+94) {
		tmp = t * ((a * -4.0) / c);
	} else {
		tmp = 9.0 * ((x * (y / c)) / z);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = y * (9.0 * x)
	tmp = 0
	if t_1 <= -2e+121:
		tmp = x * ((y / c) / (z / 9.0))
	elif t_1 <= -5e-233:
		tmp = a * ((t * -4.0) / c)
	elif t_1 <= 4e-299:
		tmp = 1.0 / ((z * c) / b)
	elif t_1 <= 1e+94:
		tmp = t * ((a * -4.0) / c)
	else:
		tmp = 9.0 * ((x * (y / c)) / z)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(9.0 * x))
	tmp = 0.0
	if (t_1 <= -2e+121)
		tmp = Float64(x * Float64(Float64(y / c) / Float64(z / 9.0)));
	elseif (t_1 <= -5e-233)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c));
	elseif (t_1 <= 4e-299)
		tmp = Float64(1.0 / Float64(Float64(z * c) / b));
	elseif (t_1 <= 1e+94)
		tmp = Float64(t * Float64(Float64(a * -4.0) / c));
	else
		tmp = Float64(9.0 * Float64(Float64(x * Float64(y / c)) / z));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = y * (9.0 * x);
	tmp = 0.0;
	if (t_1 <= -2e+121)
		tmp = x * ((y / c) / (z / 9.0));
	elseif (t_1 <= -5e-233)
		tmp = a * ((t * -4.0) / c);
	elseif (t_1 <= 4e-299)
		tmp = 1.0 / ((z * c) / b);
	elseif (t_1 <= 1e+94)
		tmp = t * ((a * -4.0) / c);
	else
		tmp = 9.0 * ((x * (y / c)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+121], N[(x * N[(N[(y / c), $MachinePrecision] / N[(z / 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-233], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e-299], N[(1.0 / N[(N[(z * c), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+94], N[(t * N[(N[(a * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.00000000000000007e121

   1. Initial program 68.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 68.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 68.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 70.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 70.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 70.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 72.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 58.1%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 58.1%

         \[\leadsto \color{blue}{\frac{x \cdot y}{c \cdot z} \cdot 9} \]

      2. associate-/l* 70.7%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \cdot 9 \]

      3. associate-*l* 70.7%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right)} \]

      4. *-commutative 70.7%

         \[\leadsto x \cdot \color{blue}{\left(9 \cdot \frac{y}{c \cdot z}\right)} \]

      5. associate-*r/ 70.7%

         \[\leadsto x \cdot \color{blue}{\frac{9 \cdot y}{c \cdot z}} \]

      6. *-commutative 70.7%

         \[\leadsto x \cdot \frac{\color{blue}{y \cdot 9}}{c \cdot z} \]

      7. associate-/l* 70.5%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot \frac{9}{c \cdot z}\right)} \]

      8. *-commutative 70.5%

         \[\leadsto x \cdot \left(y \cdot \frac{9}{\color{blue}{z \cdot c}}\right) \]

   7. Simplified 70.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{9}{z \cdot c}\right)} \]
   8. Step-by-step derivation

      1. clear-num 70.6%

         \[\leadsto x \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{z \cdot c}{9}}}\right) \]

      2. inv-pow 70.6%

         \[\leadsto x \cdot \left(y \cdot \color{blue}{{\left(\frac{z \cdot c}{9}\right)}^{-1}}\right) \]

      3. *-commutative 70.6%

         \[\leadsto x \cdot \left(y \cdot {\left(\frac{\color{blue}{c \cdot z}}{9}\right)}^{-1}\right) \]

   9. Applied egg-rr 70.6%

      \[\leadsto x \cdot \left(y \cdot \color{blue}{{\left(\frac{c \cdot z}{9}\right)}^{-1}}\right) \]
   10. Step-by-step derivation

       1. unpow-1 70.6%

          \[\leadsto x \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{c \cdot z}{9}}}\right) \]

   11. Simplified 70.6%

       \[\leadsto x \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{c \cdot z}{9}}}\right) \]
   12. Step-by-step derivation

       1. pow1 70.6%

          \[\leadsto \color{blue}{{\left(x \cdot \left(y \cdot \frac{1}{\frac{c \cdot z}{9}}\right)\right)}^{1}} \]

       2. un-div-inv 70.7%

          \[\leadsto {\left(x \cdot \color{blue}{\frac{y}{\frac{c \cdot z}{9}}}\right)}^{1} \]

       3. associate-/l* 70.7%

          \[\leadsto {\left(x \cdot \frac{y}{\color{blue}{c \cdot \frac{z}{9}}}\right)}^{1} \]

   13. Applied egg-rr 70.7%

       \[\leadsto \color{blue}{{\left(x \cdot \frac{y}{c \cdot \frac{z}{9}}\right)}^{1}} \]
   14. Step-by-step derivation

       1. unpow1 70.7%

          \[\leadsto \color{blue}{x \cdot \frac{y}{c \cdot \frac{z}{9}}} \]

       2. associate-/r* 76.7%

          \[\leadsto x \cdot \color{blue}{\frac{\frac{y}{c}}{\frac{z}{9}}} \]

   15. Simplified 76.7%

       \[\leadsto \color{blue}{x \cdot \frac{\frac{y}{c}}{\frac{z}{9}}} \]

   if -2.00000000000000007e121 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000012e-233

   1. Initial program 74.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 74.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 74.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 69.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 69.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 69.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 68.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 47.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 47.8%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 51.3%

         \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right)} \cdot -4 \]

      3. associate-*r* 51.3%

         \[\leadsto \color{blue}{a \cdot \left(\frac{t}{c} \cdot -4\right)} \]

      4. *-commutative 51.3%

         \[\leadsto a \cdot \color{blue}{\left(-4 \cdot \frac{t}{c}\right)} \]

      5. *-commutative 51.3%

         \[\leadsto a \cdot \color{blue}{\left(\frac{t}{c} \cdot -4\right)} \]

      6. associate-*l/ 51.3%

         \[\leadsto a \cdot \color{blue}{\frac{t \cdot -4}{c}} \]

   7. Simplified 51.3%

      \[\leadsto \color{blue}{a \cdot \frac{t \cdot -4}{c}} \]

   if -5.00000000000000012e-233 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 3.99999999999999997e-299

   1. Initial program 90.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 90.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 90.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 87.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 87.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 87.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 87.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 60.5%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 60.5%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 60.5%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   8. Step-by-step derivation

      1. *-commutative 60.5%

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

      2. clear-num 60.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{c \cdot z}{b}}} \]

      3. inv-pow 60.6%

         \[\leadsto \color{blue}{{\left(\frac{c \cdot z}{b}\right)}^{-1}} \]

   9. Applied egg-rr 60.6%

      \[\leadsto \color{blue}{{\left(\frac{c \cdot z}{b}\right)}^{-1}} \]
   10. Step-by-step derivation

       1. unpow-1 60.6%

          \[\leadsto \color{blue}{\frac{1}{\frac{c \cdot z}{b}}} \]

   11. Simplified 60.6%

       \[\leadsto \color{blue}{\frac{1}{\frac{c \cdot z}{b}}} \]

   if 3.99999999999999997e-299 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e94

   1. Initial program 85.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 85.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 85.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 86.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 86.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 86.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 86.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 84.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 84.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 84.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 87.7%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   6. Taylor expanded in z around inf 64.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. associate-*r/ 64.3%

         \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

      2. associate-*r* 64.3%

         \[\leadsto \frac{\color{blue}{\left(-4 \cdot a\right) \cdot t}}{c} \]

      3. associate-*l/ 66.9%

         \[\leadsto \color{blue}{\frac{-4 \cdot a}{c} \cdot t} \]

      4. *-commutative 66.9%

         \[\leadsto \frac{\color{blue}{a \cdot -4}}{c} \cdot t \]

   8. Simplified 66.9%

      \[\leadsto \color{blue}{\frac{a \cdot -4}{c} \cdot t} \]

   if 1e94 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 72.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 72.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 72.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 70.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 70.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 70.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 70.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 51.0%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/l* 54.9%

         \[\leadsto 9 \cdot \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \]

   7. Applied egg-rr 54.9%

      \[\leadsto 9 \cdot \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \]
   8. Step-by-step derivation

      1. associate-/r* 60.5%

         \[\leadsto 9 \cdot \left(x \cdot \color{blue}{\frac{\frac{y}{c}}{z}}\right) \]

      2. associate-*r/ 60.7%

         \[\leadsto 9 \cdot \color{blue}{\frac{x \cdot \frac{y}{c}}{z}} \]

   9. Simplified 60.7%

      \[\leadsto 9 \cdot \color{blue}{\frac{x \cdot \frac{y}{c}}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(9 \cdot x\right) \leq -2 \cdot 10^{+121}:\\ \;\;\;\;x \cdot \frac{\frac{y}{c}}{\frac{z}{9}}\\ \mathbf{elif}\;y \cdot \left(9 \cdot x\right) \leq -5 \cdot 10^{-233}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;y \cdot \left(9 \cdot x\right) \leq 4 \cdot 10^{-299}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b}}\\ \mathbf{elif}\;y \cdot \left(9 \cdot x\right) \leq 10^{+94}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x \cdot \frac{y}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 54.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(9 \cdot x\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+121}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-233}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-299}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b}}\\ \mathbf{elif}\;t\_1 \leq 10^{+94}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x \cdot \frac{y}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* 9.0 x))))
   (if (<= t_1 -2e+121)
     (* 9.0 (* (/ y c) (/ x z)))
     (if (<= t_1 -5e-233)
       (* a (/ (* t -4.0) c))
       (if (<= t_1 4e-299)
         (/ 1.0 (/ (* z c) b))
         (if (<= t_1 1e+94)
           (* t (/ (* a -4.0) c))
           (* 9.0 (/ (* x (/ y c)) z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (9.0 * x);
	double tmp;
	if (t_1 <= -2e+121) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if (t_1 <= -5e-233) {
		tmp = a * ((t * -4.0) / c);
	} else if (t_1 <= 4e-299) {
		tmp = 1.0 / ((z * c) / b);
	} else if (t_1 <= 1e+94) {
		tmp = t * ((a * -4.0) / c);
	} else {
		tmp = 9.0 * ((x * (y / c)) / z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (9.0d0 * x)
    if (t_1 <= (-2d+121)) then
        tmp = 9.0d0 * ((y / c) * (x / z))
    else if (t_1 <= (-5d-233)) then
        tmp = a * ((t * (-4.0d0)) / c)
    else if (t_1 <= 4d-299) then
        tmp = 1.0d0 / ((z * c) / b)
    else if (t_1 <= 1d+94) then
        tmp = t * ((a * (-4.0d0)) / c)
    else
        tmp = 9.0d0 * ((x * (y / c)) / z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (9.0 * x);
	double tmp;
	if (t_1 <= -2e+121) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if (t_1 <= -5e-233) {
		tmp = a * ((t * -4.0) / c);
	} else if (t_1 <= 4e-299) {
		tmp = 1.0 / ((z * c) / b);
	} else if (t_1 <= 1e+94) {
		tmp = t * ((a * -4.0) / c);
	} else {
		tmp = 9.0 * ((x * (y / c)) / z);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = y * (9.0 * x)
	tmp = 0
	if t_1 <= -2e+121:
		tmp = 9.0 * ((y / c) * (x / z))
	elif t_1 <= -5e-233:
		tmp = a * ((t * -4.0) / c)
	elif t_1 <= 4e-299:
		tmp = 1.0 / ((z * c) / b)
	elif t_1 <= 1e+94:
		tmp = t * ((a * -4.0) / c)
	else:
		tmp = 9.0 * ((x * (y / c)) / z)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(9.0 * x))
	tmp = 0.0
	if (t_1 <= -2e+121)
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	elseif (t_1 <= -5e-233)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c));
	elseif (t_1 <= 4e-299)
		tmp = Float64(1.0 / Float64(Float64(z * c) / b));
	elseif (t_1 <= 1e+94)
		tmp = Float64(t * Float64(Float64(a * -4.0) / c));
	else
		tmp = Float64(9.0 * Float64(Float64(x * Float64(y / c)) / z));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = y * (9.0 * x);
	tmp = 0.0;
	if (t_1 <= -2e+121)
		tmp = 9.0 * ((y / c) * (x / z));
	elseif (t_1 <= -5e-233)
		tmp = a * ((t * -4.0) / c);
	elseif (t_1 <= 4e-299)
		tmp = 1.0 / ((z * c) / b);
	elseif (t_1 <= 1e+94)
		tmp = t * ((a * -4.0) / c);
	else
		tmp = 9.0 * ((x * (y / c)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+121], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-233], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e-299], N[(1.0 / N[(N[(z * c), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+94], N[(t * N[(N[(a * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.00000000000000007e121

   1. Initial program 68.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 68.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 68.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 70.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 70.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 70.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 72.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 58.1%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 58.1%

         \[\leadsto \color{blue}{\frac{x \cdot y}{c \cdot z} \cdot 9} \]

      2. associate-/l* 70.7%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \cdot 9 \]

      3. associate-*l* 70.7%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right)} \]

      4. *-commutative 70.7%

         \[\leadsto x \cdot \color{blue}{\left(9 \cdot \frac{y}{c \cdot z}\right)} \]

      5. associate-*r/ 70.7%

         \[\leadsto x \cdot \color{blue}{\frac{9 \cdot y}{c \cdot z}} \]

      6. *-commutative 70.7%

         \[\leadsto x \cdot \frac{\color{blue}{y \cdot 9}}{c \cdot z} \]

      7. associate-/l* 70.5%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot \frac{9}{c \cdot z}\right)} \]

      8. *-commutative 70.5%

         \[\leadsto x \cdot \left(y \cdot \frac{9}{\color{blue}{z \cdot c}}\right) \]

   7. Simplified 70.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{9}{z \cdot c}\right)} \]
   8. Step-by-step derivation

      1. clear-num 70.6%

         \[\leadsto x \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{z \cdot c}{9}}}\right) \]

      2. inv-pow 70.6%

         \[\leadsto x \cdot \left(y \cdot \color{blue}{{\left(\frac{z \cdot c}{9}\right)}^{-1}}\right) \]

      3. *-commutative 70.6%

         \[\leadsto x \cdot \left(y \cdot {\left(\frac{\color{blue}{c \cdot z}}{9}\right)}^{-1}\right) \]

   9. Applied egg-rr 70.6%

      \[\leadsto x \cdot \left(y \cdot \color{blue}{{\left(\frac{c \cdot z}{9}\right)}^{-1}}\right) \]
   10. Step-by-step derivation

       1. unpow-1 70.6%

          \[\leadsto x \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{c \cdot z}{9}}}\right) \]

   11. Simplified 70.6%

       \[\leadsto x \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{c \cdot z}{9}}}\right) \]

   12. Taylor expanded in x around 0 58.1%

       \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   13. Step-by-step derivation

       1. *-commutative 58.1%

          \[\leadsto 9 \cdot \frac{x \cdot y}{\color{blue}{z \cdot c}} \]

       2. times-frac 74.8%

          \[\leadsto 9 \cdot \color{blue}{\left(\frac{x}{z} \cdot \frac{y}{c}\right)} \]

   14. Simplified 74.8%

       \[\leadsto \color{blue}{9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)} \]

   if -2.00000000000000007e121 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000012e-233

   1. Initial program 74.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 74.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 74.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 69.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 69.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 69.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 68.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 47.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 47.8%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 51.3%

         \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right)} \cdot -4 \]

      3. associate-*r* 51.3%

         \[\leadsto \color{blue}{a \cdot \left(\frac{t}{c} \cdot -4\right)} \]

      4. *-commutative 51.3%

         \[\leadsto a \cdot \color{blue}{\left(-4 \cdot \frac{t}{c}\right)} \]

      5. *-commutative 51.3%

         \[\leadsto a \cdot \color{blue}{\left(\frac{t}{c} \cdot -4\right)} \]

      6. associate-*l/ 51.3%

         \[\leadsto a \cdot \color{blue}{\frac{t \cdot -4}{c}} \]

   7. Simplified 51.3%

      \[\leadsto \color{blue}{a \cdot \frac{t \cdot -4}{c}} \]

   if -5.00000000000000012e-233 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 3.99999999999999997e-299

   1. Initial program 90.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 90.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 90.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 87.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 87.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 87.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 87.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 60.5%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 60.5%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 60.5%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   8. Step-by-step derivation

      1. *-commutative 60.5%

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

      2. clear-num 60.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{c \cdot z}{b}}} \]

      3. inv-pow 60.6%

         \[\leadsto \color{blue}{{\left(\frac{c \cdot z}{b}\right)}^{-1}} \]

   9. Applied egg-rr 60.6%

      \[\leadsto \color{blue}{{\left(\frac{c \cdot z}{b}\right)}^{-1}} \]
   10. Step-by-step derivation

       1. unpow-1 60.6%

          \[\leadsto \color{blue}{\frac{1}{\frac{c \cdot z}{b}}} \]

   11. Simplified 60.6%

       \[\leadsto \color{blue}{\frac{1}{\frac{c \cdot z}{b}}} \]

   if 3.99999999999999997e-299 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e94

   1. Initial program 85.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 85.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 85.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 86.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 86.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 86.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 86.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 84.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 84.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 84.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 87.7%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   6. Taylor expanded in z around inf 64.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. associate-*r/ 64.3%

         \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

      2. associate-*r* 64.3%

         \[\leadsto \frac{\color{blue}{\left(-4 \cdot a\right) \cdot t}}{c} \]

      3. associate-*l/ 66.9%

         \[\leadsto \color{blue}{\frac{-4 \cdot a}{c} \cdot t} \]

      4. *-commutative 66.9%

         \[\leadsto \frac{\color{blue}{a \cdot -4}}{c} \cdot t \]

   8. Simplified 66.9%

      \[\leadsto \color{blue}{\frac{a \cdot -4}{c} \cdot t} \]

   if 1e94 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 72.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 72.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 72.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 70.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 70.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 70.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 70.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 51.0%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/l* 54.9%

         \[\leadsto 9 \cdot \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \]

   7. Applied egg-rr 54.9%

      \[\leadsto 9 \cdot \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \]
   8. Step-by-step derivation

      1. associate-/r* 60.5%

         \[\leadsto 9 \cdot \left(x \cdot \color{blue}{\frac{\frac{y}{c}}{z}}\right) \]

      2. associate-*r/ 60.7%

         \[\leadsto 9 \cdot \color{blue}{\frac{x \cdot \frac{y}{c}}{z}} \]

   9. Simplified 60.7%

      \[\leadsto 9 \cdot \color{blue}{\frac{x \cdot \frac{y}{c}}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(9 \cdot x\right) \leq -2 \cdot 10^{+121}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;y \cdot \left(9 \cdot x\right) \leq -5 \cdot 10^{-233}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;y \cdot \left(9 \cdot x\right) \leq 4 \cdot 10^{-299}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b}}\\ \mathbf{elif}\;y \cdot \left(9 \cdot x\right) \leq 10^{+94}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x \cdot \frac{y}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 54.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(9 \cdot x\right)\\ t_2 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+121}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-233}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-299}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b}}\\ \mathbf{elif}\;t\_1 \leq 10^{+94}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* 9.0 x))) (t_2 (* 9.0 (* (/ y c) (/ x z)))))
   (if (<= t_1 -2e+121)
     t_2
     (if (<= t_1 -5e-233)
       (* a (/ (* t -4.0) c))
       (if (<= t_1 4e-299)
         (/ 1.0 (/ (* z c) b))
         (if (<= t_1 1e+94) (* t (/ (* a -4.0) c)) t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (9.0 * x);
	double t_2 = 9.0 * ((y / c) * (x / z));
	double tmp;
	if (t_1 <= -2e+121) {
		tmp = t_2;
	} else if (t_1 <= -5e-233) {
		tmp = a * ((t * -4.0) / c);
	} else if (t_1 <= 4e-299) {
		tmp = 1.0 / ((z * c) / b);
	} else if (t_1 <= 1e+94) {
		tmp = t * ((a * -4.0) / c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (9.0d0 * x)
    t_2 = 9.0d0 * ((y / c) * (x / z))
    if (t_1 <= (-2d+121)) then
        tmp = t_2
    else if (t_1 <= (-5d-233)) then
        tmp = a * ((t * (-4.0d0)) / c)
    else if (t_1 <= 4d-299) then
        tmp = 1.0d0 / ((z * c) / b)
    else if (t_1 <= 1d+94) then
        tmp = t * ((a * (-4.0d0)) / c)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (9.0 * x);
	double t_2 = 9.0 * ((y / c) * (x / z));
	double tmp;
	if (t_1 <= -2e+121) {
		tmp = t_2;
	} else if (t_1 <= -5e-233) {
		tmp = a * ((t * -4.0) / c);
	} else if (t_1 <= 4e-299) {
		tmp = 1.0 / ((z * c) / b);
	} else if (t_1 <= 1e+94) {
		tmp = t * ((a * -4.0) / c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = y * (9.0 * x)
	t_2 = 9.0 * ((y / c) * (x / z))
	tmp = 0
	if t_1 <= -2e+121:
		tmp = t_2
	elif t_1 <= -5e-233:
		tmp = a * ((t * -4.0) / c)
	elif t_1 <= 4e-299:
		tmp = 1.0 / ((z * c) / b)
	elif t_1 <= 1e+94:
		tmp = t * ((a * -4.0) / c)
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(9.0 * x))
	t_2 = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)))
	tmp = 0.0
	if (t_1 <= -2e+121)
		tmp = t_2;
	elseif (t_1 <= -5e-233)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c));
	elseif (t_1 <= 4e-299)
		tmp = Float64(1.0 / Float64(Float64(z * c) / b));
	elseif (t_1 <= 1e+94)
		tmp = Float64(t * Float64(Float64(a * -4.0) / c));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = y * (9.0 * x);
	t_2 = 9.0 * ((y / c) * (x / z));
	tmp = 0.0;
	if (t_1 <= -2e+121)
		tmp = t_2;
	elseif (t_1 <= -5e-233)
		tmp = a * ((t * -4.0) / c);
	elseif (t_1 <= 4e-299)
		tmp = 1.0 / ((z * c) / b);
	elseif (t_1 <= 1e+94)
		tmp = t * ((a * -4.0) / c);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+121], t$95$2, If[LessEqual[t$95$1, -5e-233], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e-299], N[(1.0 / N[(N[(z * c), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+94], N[(t * N[(N[(a * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.00000000000000007e121 or 1e94 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 70.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 70.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 70.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 70.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 70.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 70.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 71.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 54.7%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 54.7%

         \[\leadsto \color{blue}{\frac{x \cdot y}{c \cdot z} \cdot 9} \]

      2. associate-/l* 63.1%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \cdot 9 \]

      3. associate-*l* 63.1%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right)} \]

      4. *-commutative 63.1%

         \[\leadsto x \cdot \color{blue}{\left(9 \cdot \frac{y}{c \cdot z}\right)} \]

      5. associate-*r/ 63.1%

         \[\leadsto x \cdot \color{blue}{\frac{9 \cdot y}{c \cdot z}} \]

      6. *-commutative 63.1%

         \[\leadsto x \cdot \frac{\color{blue}{y \cdot 9}}{c \cdot z} \]

      7. associate-/l* 63.0%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot \frac{9}{c \cdot z}\right)} \]

      8. *-commutative 63.0%

         \[\leadsto x \cdot \left(y \cdot \frac{9}{\color{blue}{z \cdot c}}\right) \]

   7. Simplified 63.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{9}{z \cdot c}\right)} \]
   8. Step-by-step derivation

      1. clear-num 63.0%

         \[\leadsto x \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{z \cdot c}{9}}}\right) \]

      2. inv-pow 63.0%

         \[\leadsto x \cdot \left(y \cdot \color{blue}{{\left(\frac{z \cdot c}{9}\right)}^{-1}}\right) \]

      3. *-commutative 63.0%

         \[\leadsto x \cdot \left(y \cdot {\left(\frac{\color{blue}{c \cdot z}}{9}\right)}^{-1}\right) \]

   9. Applied egg-rr 63.0%

      \[\leadsto x \cdot \left(y \cdot \color{blue}{{\left(\frac{c \cdot z}{9}\right)}^{-1}}\right) \]
   10. Step-by-step derivation

       1. unpow-1 63.0%

          \[\leadsto x \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{c \cdot z}{9}}}\right) \]

   11. Simplified 63.0%

       \[\leadsto x \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{c \cdot z}{9}}}\right) \]

   12. Taylor expanded in x around 0 54.7%

       \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   13. Step-by-step derivation

       1. *-commutative 54.7%

          \[\leadsto 9 \cdot \frac{x \cdot y}{\color{blue}{z \cdot c}} \]

       2. times-frac 69.3%

          \[\leadsto 9 \cdot \color{blue}{\left(\frac{x}{z} \cdot \frac{y}{c}\right)} \]

   14. Simplified 69.3%

       \[\leadsto \color{blue}{9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)} \]

   if -2.00000000000000007e121 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000012e-233

   1. Initial program 74.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 74.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 74.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 69.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 69.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 69.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 68.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 47.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 47.8%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 51.3%

         \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right)} \cdot -4 \]

      3. associate-*r* 51.3%

         \[\leadsto \color{blue}{a \cdot \left(\frac{t}{c} \cdot -4\right)} \]

      4. *-commutative 51.3%

         \[\leadsto a \cdot \color{blue}{\left(-4 \cdot \frac{t}{c}\right)} \]

      5. *-commutative 51.3%

         \[\leadsto a \cdot \color{blue}{\left(\frac{t}{c} \cdot -4\right)} \]

      6. associate-*l/ 51.3%

         \[\leadsto a \cdot \color{blue}{\frac{t \cdot -4}{c}} \]

   7. Simplified 51.3%

      \[\leadsto \color{blue}{a \cdot \frac{t \cdot -4}{c}} \]

   if -5.00000000000000012e-233 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 3.99999999999999997e-299

   1. Initial program 90.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 90.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 90.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 87.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 87.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 87.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 87.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 60.5%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 60.5%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 60.5%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   8. Step-by-step derivation

      1. *-commutative 60.5%

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

      2. clear-num 60.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{c \cdot z}{b}}} \]

      3. inv-pow 60.6%

         \[\leadsto \color{blue}{{\left(\frac{c \cdot z}{b}\right)}^{-1}} \]

   9. Applied egg-rr 60.6%

      \[\leadsto \color{blue}{{\left(\frac{c \cdot z}{b}\right)}^{-1}} \]
   10. Step-by-step derivation

       1. unpow-1 60.6%

          \[\leadsto \color{blue}{\frac{1}{\frac{c \cdot z}{b}}} \]

   11. Simplified 60.6%

       \[\leadsto \color{blue}{\frac{1}{\frac{c \cdot z}{b}}} \]

   if 3.99999999999999997e-299 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e94

   1. Initial program 85.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 85.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 85.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 86.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 86.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 86.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 86.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 84.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 84.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 84.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 87.7%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   6. Taylor expanded in z around inf 64.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. associate-*r/ 64.3%

         \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

      2. associate-*r* 64.3%

         \[\leadsto \frac{\color{blue}{\left(-4 \cdot a\right) \cdot t}}{c} \]

      3. associate-*l/ 66.9%

         \[\leadsto \color{blue}{\frac{-4 \cdot a}{c} \cdot t} \]

      4. *-commutative 66.9%

         \[\leadsto \frac{\color{blue}{a \cdot -4}}{c} \cdot t \]

   8. Simplified 66.9%

      \[\leadsto \color{blue}{\frac{a \cdot -4}{c} \cdot t} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(9 \cdot x\right) \leq -2 \cdot 10^{+121}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;y \cdot \left(9 \cdot x\right) \leq -5 \cdot 10^{-233}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;y \cdot \left(9 \cdot x\right) \leq 4 \cdot 10^{-299}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b}}\\ \mathbf{elif}\;y \cdot \left(9 \cdot x\right) \leq 10^{+94}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 54.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(9 \cdot x\right)\\ t_2 := 9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+121}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-233}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-299}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b}}\\ \mathbf{elif}\;t\_1 \leq 10^{+94}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* 9.0 x))) (t_2 (* 9.0 (* x (/ y (* z c))))))
   (if (<= t_1 -2e+121)
     t_2
     (if (<= t_1 -5e-233)
       (* a (/ (* t -4.0) c))
       (if (<= t_1 4e-299)
         (/ 1.0 (/ (* z c) b))
         (if (<= t_1 1e+94) (* t (/ (* a -4.0) c)) t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (9.0 * x);
	double t_2 = 9.0 * (x * (y / (z * c)));
	double tmp;
	if (t_1 <= -2e+121) {
		tmp = t_2;
	} else if (t_1 <= -5e-233) {
		tmp = a * ((t * -4.0) / c);
	} else if (t_1 <= 4e-299) {
		tmp = 1.0 / ((z * c) / b);
	} else if (t_1 <= 1e+94) {
		tmp = t * ((a * -4.0) / c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (9.0d0 * x)
    t_2 = 9.0d0 * (x * (y / (z * c)))
    if (t_1 <= (-2d+121)) then
        tmp = t_2
    else if (t_1 <= (-5d-233)) then
        tmp = a * ((t * (-4.0d0)) / c)
    else if (t_1 <= 4d-299) then
        tmp = 1.0d0 / ((z * c) / b)
    else if (t_1 <= 1d+94) then
        tmp = t * ((a * (-4.0d0)) / c)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (9.0 * x);
	double t_2 = 9.0 * (x * (y / (z * c)));
	double tmp;
	if (t_1 <= -2e+121) {
		tmp = t_2;
	} else if (t_1 <= -5e-233) {
		tmp = a * ((t * -4.0) / c);
	} else if (t_1 <= 4e-299) {
		tmp = 1.0 / ((z * c) / b);
	} else if (t_1 <= 1e+94) {
		tmp = t * ((a * -4.0) / c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = y * (9.0 * x)
	t_2 = 9.0 * (x * (y / (z * c)))
	tmp = 0
	if t_1 <= -2e+121:
		tmp = t_2
	elif t_1 <= -5e-233:
		tmp = a * ((t * -4.0) / c)
	elif t_1 <= 4e-299:
		tmp = 1.0 / ((z * c) / b)
	elif t_1 <= 1e+94:
		tmp = t * ((a * -4.0) / c)
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(9.0 * x))
	t_2 = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))))
	tmp = 0.0
	if (t_1 <= -2e+121)
		tmp = t_2;
	elseif (t_1 <= -5e-233)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c));
	elseif (t_1 <= 4e-299)
		tmp = Float64(1.0 / Float64(Float64(z * c) / b));
	elseif (t_1 <= 1e+94)
		tmp = Float64(t * Float64(Float64(a * -4.0) / c));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = y * (9.0 * x);
	t_2 = 9.0 * (x * (y / (z * c)));
	tmp = 0.0;
	if (t_1 <= -2e+121)
		tmp = t_2;
	elseif (t_1 <= -5e-233)
		tmp = a * ((t * -4.0) / c);
	elseif (t_1 <= 4e-299)
		tmp = 1.0 / ((z * c) / b);
	elseif (t_1 <= 1e+94)
		tmp = t * ((a * -4.0) / c);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+121], t$95$2, If[LessEqual[t$95$1, -5e-233], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e-299], N[(1.0 / N[(N[(z * c), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+94], N[(t * N[(N[(a * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.00000000000000007e121 or 1e94 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 70.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 70.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 70.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 70.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 70.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 70.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 71.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 54.7%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/l* 63.1%

         \[\leadsto 9 \cdot \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \]

      2. *-commutative 63.1%

         \[\leadsto 9 \cdot \left(x \cdot \frac{y}{\color{blue}{z \cdot c}}\right) \]

   7. Simplified 63.1%

      \[\leadsto \color{blue}{9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)} \]

   if -2.00000000000000007e121 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000012e-233

   1. Initial program 74.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 74.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 74.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 69.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 69.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 69.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 68.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 47.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 47.8%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 51.3%

         \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right)} \cdot -4 \]

      3. associate-*r* 51.3%

         \[\leadsto \color{blue}{a \cdot \left(\frac{t}{c} \cdot -4\right)} \]

      4. *-commutative 51.3%

         \[\leadsto a \cdot \color{blue}{\left(-4 \cdot \frac{t}{c}\right)} \]

      5. *-commutative 51.3%

         \[\leadsto a \cdot \color{blue}{\left(\frac{t}{c} \cdot -4\right)} \]

      6. associate-*l/ 51.3%

         \[\leadsto a \cdot \color{blue}{\frac{t \cdot -4}{c}} \]

   7. Simplified 51.3%

      \[\leadsto \color{blue}{a \cdot \frac{t \cdot -4}{c}} \]

   if -5.00000000000000012e-233 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 3.99999999999999997e-299

   1. Initial program 90.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 90.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 90.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 87.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 87.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 87.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 87.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 60.5%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 60.5%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 60.5%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   8. Step-by-step derivation

      1. *-commutative 60.5%

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

      2. clear-num 60.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{c \cdot z}{b}}} \]

      3. inv-pow 60.6%

         \[\leadsto \color{blue}{{\left(\frac{c \cdot z}{b}\right)}^{-1}} \]

   9. Applied egg-rr 60.6%

      \[\leadsto \color{blue}{{\left(\frac{c \cdot z}{b}\right)}^{-1}} \]
   10. Step-by-step derivation

       1. unpow-1 60.6%

          \[\leadsto \color{blue}{\frac{1}{\frac{c \cdot z}{b}}} \]

   11. Simplified 60.6%

       \[\leadsto \color{blue}{\frac{1}{\frac{c \cdot z}{b}}} \]

   if 3.99999999999999997e-299 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e94

   1. Initial program 85.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 85.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 85.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 86.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 86.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 86.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 86.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 84.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 84.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 84.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 87.7%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   6. Taylor expanded in z around inf 64.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. associate-*r/ 64.3%

         \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

      2. associate-*r* 64.3%

         \[\leadsto \frac{\color{blue}{\left(-4 \cdot a\right) \cdot t}}{c} \]

      3. associate-*l/ 66.9%

         \[\leadsto \color{blue}{\frac{-4 \cdot a}{c} \cdot t} \]

      4. *-commutative 66.9%

         \[\leadsto \frac{\color{blue}{a \cdot -4}}{c} \cdot t \]

   8. Simplified 66.9%

      \[\leadsto \color{blue}{\frac{a \cdot -4}{c} \cdot t} \]
3. Recombined 4 regimes into one program.

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(9 \cdot x\right) \leq -2 \cdot 10^{+121}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;y \cdot \left(9 \cdot x\right) \leq -5 \cdot 10^{-233}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;y \cdot \left(9 \cdot x\right) \leq 4 \cdot 10^{-299}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b}}\\ \mathbf{elif}\;y \cdot \left(9 \cdot x\right) \leq 10^{+94}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(9 \cdot x\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+133}:\\ \;\;\;\;x \cdot \frac{\frac{y}{c}}{\frac{z}{9}}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+109}:\\ \;\;\;\;\frac{b}{z \cdot c} - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+225}:\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \frac{y \cdot x}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot \frac{9}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* 9.0 x))))
   (if (<= t_1 -1e+133)
     (* x (/ (/ y c) (/ z 9.0)))
     (if (<= t_1 2e+109)
       (- (/ b (* z c)) (* 4.0 (/ (* a t) c)))
       (if (<= t_1 2e+225)
         (/ (+ (/ b z) (* 9.0 (/ (* y x) z))) c)
         (* x (/ (* y (/ 9.0 z)) c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (9.0 * x);
	double tmp;
	if (t_1 <= -1e+133) {
		tmp = x * ((y / c) / (z / 9.0));
	} else if (t_1 <= 2e+109) {
		tmp = (b / (z * c)) - (4.0 * ((a * t) / c));
	} else if (t_1 <= 2e+225) {
		tmp = ((b / z) + (9.0 * ((y * x) / z))) / c;
	} else {
		tmp = x * ((y * (9.0 / z)) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (9.0d0 * x)
    if (t_1 <= (-1d+133)) then
        tmp = x * ((y / c) / (z / 9.0d0))
    else if (t_1 <= 2d+109) then
        tmp = (b / (z * c)) - (4.0d0 * ((a * t) / c))
    else if (t_1 <= 2d+225) then
        tmp = ((b / z) + (9.0d0 * ((y * x) / z))) / c
    else
        tmp = x * ((y * (9.0d0 / z)) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (9.0 * x);
	double tmp;
	if (t_1 <= -1e+133) {
		tmp = x * ((y / c) / (z / 9.0));
	} else if (t_1 <= 2e+109) {
		tmp = (b / (z * c)) - (4.0 * ((a * t) / c));
	} else if (t_1 <= 2e+225) {
		tmp = ((b / z) + (9.0 * ((y * x) / z))) / c;
	} else {
		tmp = x * ((y * (9.0 / z)) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = y * (9.0 * x)
	tmp = 0
	if t_1 <= -1e+133:
		tmp = x * ((y / c) / (z / 9.0))
	elif t_1 <= 2e+109:
		tmp = (b / (z * c)) - (4.0 * ((a * t) / c))
	elif t_1 <= 2e+225:
		tmp = ((b / z) + (9.0 * ((y * x) / z))) / c
	else:
		tmp = x * ((y * (9.0 / z)) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(9.0 * x))
	tmp = 0.0
	if (t_1 <= -1e+133)
		tmp = Float64(x * Float64(Float64(y / c) / Float64(z / 9.0)));
	elseif (t_1 <= 2e+109)
		tmp = Float64(Float64(b / Float64(z * c)) - Float64(4.0 * Float64(Float64(a * t) / c)));
	elseif (t_1 <= 2e+225)
		tmp = Float64(Float64(Float64(b / z) + Float64(9.0 * Float64(Float64(y * x) / z))) / c);
	else
		tmp = Float64(x * Float64(Float64(y * Float64(9.0 / z)) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = y * (9.0 * x);
	tmp = 0.0;
	if (t_1 <= -1e+133)
		tmp = x * ((y / c) / (z / 9.0));
	elseif (t_1 <= 2e+109)
		tmp = (b / (z * c)) - (4.0 * ((a * t) / c));
	elseif (t_1 <= 2e+225)
		tmp = ((b / z) + (9.0 * ((y * x) / z))) / c;
	else
		tmp = x * ((y * (9.0 / z)) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+133], N[(x * N[(N[(y / c), $MachinePrecision] / N[(z / 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+109], N[(N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+225], N[(N[(N[(b / z), $MachinePrecision] + N[(9.0 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(x * N[(N[(y * N[(9.0 / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e133

   1. Initial program 68.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 68.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 68.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 70.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 70.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 70.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 72.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 59.4%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 59.4%

         \[\leadsto \color{blue}{\frac{x \cdot y}{c \cdot z} \cdot 9} \]

      2. associate-/l* 72.7%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \cdot 9 \]

      3. associate-*l* 72.8%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right)} \]

      4. *-commutative 72.8%

         \[\leadsto x \cdot \color{blue}{\left(9 \cdot \frac{y}{c \cdot z}\right)} \]

      5. associate-*r/ 72.7%

         \[\leadsto x \cdot \color{blue}{\frac{9 \cdot y}{c \cdot z}} \]

      6. *-commutative 72.7%

         \[\leadsto x \cdot \frac{\color{blue}{y \cdot 9}}{c \cdot z} \]

      7. associate-/l* 72.6%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot \frac{9}{c \cdot z}\right)} \]

      8. *-commutative 72.6%

         \[\leadsto x \cdot \left(y \cdot \frac{9}{\color{blue}{z \cdot c}}\right) \]

   7. Simplified 72.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{9}{z \cdot c}\right)} \]
   8. Step-by-step derivation

      1. clear-num 72.6%

         \[\leadsto x \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{z \cdot c}{9}}}\right) \]

      2. inv-pow 72.6%

         \[\leadsto x \cdot \left(y \cdot \color{blue}{{\left(\frac{z \cdot c}{9}\right)}^{-1}}\right) \]

      3. *-commutative 72.6%

         \[\leadsto x \cdot \left(y \cdot {\left(\frac{\color{blue}{c \cdot z}}{9}\right)}^{-1}\right) \]

   9. Applied egg-rr 72.6%

      \[\leadsto x \cdot \left(y \cdot \color{blue}{{\left(\frac{c \cdot z}{9}\right)}^{-1}}\right) \]
   10. Step-by-step derivation

       1. unpow-1 72.6%

          \[\leadsto x \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{c \cdot z}{9}}}\right) \]

   11. Simplified 72.6%

       \[\leadsto x \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{c \cdot z}{9}}}\right) \]
   12. Step-by-step derivation

       1. pow1 72.6%

          \[\leadsto \color{blue}{{\left(x \cdot \left(y \cdot \frac{1}{\frac{c \cdot z}{9}}\right)\right)}^{1}} \]

       2. un-div-inv 72.8%

          \[\leadsto {\left(x \cdot \color{blue}{\frac{y}{\frac{c \cdot z}{9}}}\right)}^{1} \]

       3. associate-/l* 72.7%

          \[\leadsto {\left(x \cdot \frac{y}{\color{blue}{c \cdot \frac{z}{9}}}\right)}^{1} \]

   13. Applied egg-rr 72.7%

       \[\leadsto \color{blue}{{\left(x \cdot \frac{y}{c \cdot \frac{z}{9}}\right)}^{1}} \]
   14. Step-by-step derivation

       1. unpow1 72.7%

          \[\leadsto \color{blue}{x \cdot \frac{y}{c \cdot \frac{z}{9}}} \]

       2. associate-/r* 77.3%

          \[\leadsto x \cdot \color{blue}{\frac{\frac{y}{c}}{\frac{z}{9}}} \]

   15. Simplified 77.3%

       \[\leadsto \color{blue}{x \cdot \frac{\frac{y}{c}}{\frac{z}{9}}} \]

   if -1e133 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999996e109

   1. Initial program 83.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 83.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 83.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 81.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 81.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 81.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 81.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 82.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 82.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 82.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 89.6%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   6. Taylor expanded in x around 0 84.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} - 4 \cdot \frac{a \cdot t}{c} \]

   if 1.99999999999999996e109 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999986e225

   1. Initial program 77.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 77.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 77.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 77.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 82.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 82.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 82.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 82.2%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   6. Taylor expanded in c around 0 90.9%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   7. Taylor expanded in a around 0 68.8%

      \[\leadsto \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}}{c}} \]

   if 1.99999999999999986e225 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 60.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 60.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 60.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 56.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 56.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 56.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 56.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 56.3%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 56.3%

         \[\leadsto \color{blue}{\frac{x \cdot y}{c \cdot z} \cdot 9} \]

      2. associate-/l* 69.1%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \cdot 9 \]

      3. associate-*l* 69.0%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right)} \]

      4. *-commutative 69.0%

         \[\leadsto x \cdot \color{blue}{\left(9 \cdot \frac{y}{c \cdot z}\right)} \]

      5. associate-*r/ 69.0%

         \[\leadsto x \cdot \color{blue}{\frac{9 \cdot y}{c \cdot z}} \]

      6. *-commutative 69.0%

         \[\leadsto x \cdot \frac{\color{blue}{y \cdot 9}}{c \cdot z} \]

      7. associate-/l* 69.0%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot \frac{9}{c \cdot z}\right)} \]

      8. *-commutative 69.0%

         \[\leadsto x \cdot \left(y \cdot \frac{9}{\color{blue}{z \cdot c}}\right) \]

   7. Simplified 69.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{9}{z \cdot c}\right)} \]

   8. Taylor expanded in y around 0 69.0%

      \[\leadsto x \cdot \color{blue}{\left(9 \cdot \frac{y}{c \cdot z}\right)} \]
   9. Step-by-step derivation

      1. associate-*r/ 69.0%

         \[\leadsto x \cdot \color{blue}{\frac{9 \cdot y}{c \cdot z}} \]

      2. *-commutative 69.0%

         \[\leadsto x \cdot \frac{\color{blue}{y \cdot 9}}{c \cdot z} \]

      3. times-frac 77.8%

         \[\leadsto x \cdot \color{blue}{\left(\frac{y}{c} \cdot \frac{9}{z}\right)} \]

      4. associate-*l/ 73.6%

         \[\leadsto x \cdot \color{blue}{\frac{y \cdot \frac{9}{z}}{c}} \]

   10. Simplified 73.6%

       \[\leadsto x \cdot \color{blue}{\frac{y \cdot \frac{9}{z}}{c}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(9 \cdot x\right) \leq -1 \cdot 10^{+133}:\\ \;\;\;\;x \cdot \frac{\frac{y}{c}}{\frac{z}{9}}\\ \mathbf{elif}\;y \cdot \left(9 \cdot x\right) \leq 2 \cdot 10^{+109}:\\ \;\;\;\;\frac{b}{z \cdot c} - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;y \cdot \left(9 \cdot x\right) \leq 2 \cdot 10^{+225}:\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \frac{y \cdot x}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot \frac{9}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(9 \cdot x\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+133}:\\ \;\;\;\;x \cdot \frac{\frac{y}{c}}{\frac{z}{9}}\\ \mathbf{elif}\;t\_1 \leq 10^{+94}:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+193}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot \frac{9}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* 9.0 x))))
   (if (<= t_1 -1e+133)
     (* x (/ (/ y c) (/ z 9.0)))
     (if (<= t_1 1e+94)
       (/ (- (/ b z) (* 4.0 (* a t))) c)
       (if (<= t_1 5e+193)
         (/ (+ b (* 9.0 (* y x))) (* z c))
         (* x (/ (* y (/ 9.0 z)) c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (9.0 * x);
	double tmp;
	if (t_1 <= -1e+133) {
		tmp = x * ((y / c) / (z / 9.0));
	} else if (t_1 <= 1e+94) {
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	} else if (t_1 <= 5e+193) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = x * ((y * (9.0 / z)) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (9.0d0 * x)
    if (t_1 <= (-1d+133)) then
        tmp = x * ((y / c) / (z / 9.0d0))
    else if (t_1 <= 1d+94) then
        tmp = ((b / z) - (4.0d0 * (a * t))) / c
    else if (t_1 <= 5d+193) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c)
    else
        tmp = x * ((y * (9.0d0 / z)) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (9.0 * x);
	double tmp;
	if (t_1 <= -1e+133) {
		tmp = x * ((y / c) / (z / 9.0));
	} else if (t_1 <= 1e+94) {
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	} else if (t_1 <= 5e+193) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = x * ((y * (9.0 / z)) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = y * (9.0 * x)
	tmp = 0
	if t_1 <= -1e+133:
		tmp = x * ((y / c) / (z / 9.0))
	elif t_1 <= 1e+94:
		tmp = ((b / z) - (4.0 * (a * t))) / c
	elif t_1 <= 5e+193:
		tmp = (b + (9.0 * (y * x))) / (z * c)
	else:
		tmp = x * ((y * (9.0 / z)) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(9.0 * x))
	tmp = 0.0
	if (t_1 <= -1e+133)
		tmp = Float64(x * Float64(Float64(y / c) / Float64(z / 9.0)));
	elseif (t_1 <= 1e+94)
		tmp = Float64(Float64(Float64(b / z) - Float64(4.0 * Float64(a * t))) / c);
	elseif (t_1 <= 5e+193)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c));
	else
		tmp = Float64(x * Float64(Float64(y * Float64(9.0 / z)) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = y * (9.0 * x);
	tmp = 0.0;
	if (t_1 <= -1e+133)
		tmp = x * ((y / c) / (z / 9.0));
	elseif (t_1 <= 1e+94)
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	elseif (t_1 <= 5e+193)
		tmp = (b + (9.0 * (y * x))) / (z * c);
	else
		tmp = x * ((y * (9.0 / z)) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+133], N[(x * N[(N[(y / c), $MachinePrecision] / N[(z / 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+94], N[(N[(N[(b / z), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 5e+193], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * N[(9.0 / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e133

   1. Initial program 68.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 68.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 68.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 70.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 70.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 70.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 72.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 59.4%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 59.4%

         \[\leadsto \color{blue}{\frac{x \cdot y}{c \cdot z} \cdot 9} \]

      2. associate-/l* 72.7%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \cdot 9 \]

      3. associate-*l* 72.8%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right)} \]

      4. *-commutative 72.8%

         \[\leadsto x \cdot \color{blue}{\left(9 \cdot \frac{y}{c \cdot z}\right)} \]

      5. associate-*r/ 72.7%

         \[\leadsto x \cdot \color{blue}{\frac{9 \cdot y}{c \cdot z}} \]

      6. *-commutative 72.7%

         \[\leadsto x \cdot \frac{\color{blue}{y \cdot 9}}{c \cdot z} \]

      7. associate-/l* 72.6%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot \frac{9}{c \cdot z}\right)} \]

      8. *-commutative 72.6%

         \[\leadsto x \cdot \left(y \cdot \frac{9}{\color{blue}{z \cdot c}}\right) \]

   7. Simplified 72.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{9}{z \cdot c}\right)} \]
   8. Step-by-step derivation

      1. clear-num 72.6%

         \[\leadsto x \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{z \cdot c}{9}}}\right) \]

      2. inv-pow 72.6%

         \[\leadsto x \cdot \left(y \cdot \color{blue}{{\left(\frac{z \cdot c}{9}\right)}^{-1}}\right) \]

      3. *-commutative 72.6%

         \[\leadsto x \cdot \left(y \cdot {\left(\frac{\color{blue}{c \cdot z}}{9}\right)}^{-1}\right) \]

   9. Applied egg-rr 72.6%

      \[\leadsto x \cdot \left(y \cdot \color{blue}{{\left(\frac{c \cdot z}{9}\right)}^{-1}}\right) \]
   10. Step-by-step derivation

       1. unpow-1 72.6%

          \[\leadsto x \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{c \cdot z}{9}}}\right) \]

   11. Simplified 72.6%

       \[\leadsto x \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{c \cdot z}{9}}}\right) \]
   12. Step-by-step derivation

       1. pow1 72.6%

          \[\leadsto \color{blue}{{\left(x \cdot \left(y \cdot \frac{1}{\frac{c \cdot z}{9}}\right)\right)}^{1}} \]

       2. un-div-inv 72.8%

          \[\leadsto {\left(x \cdot \color{blue}{\frac{y}{\frac{c \cdot z}{9}}}\right)}^{1} \]

       3. associate-/l* 72.7%

          \[\leadsto {\left(x \cdot \frac{y}{\color{blue}{c \cdot \frac{z}{9}}}\right)}^{1} \]

   13. Applied egg-rr 72.7%

       \[\leadsto \color{blue}{{\left(x \cdot \frac{y}{c \cdot \frac{z}{9}}\right)}^{1}} \]
   14. Step-by-step derivation

       1. unpow1 72.7%

          \[\leadsto \color{blue}{x \cdot \frac{y}{c \cdot \frac{z}{9}}} \]

       2. associate-/r* 77.3%

          \[\leadsto x \cdot \color{blue}{\frac{\frac{y}{c}}{\frac{z}{9}}} \]

   15. Simplified 77.3%

       \[\leadsto \color{blue}{x \cdot \frac{\frac{y}{c}}{\frac{z}{9}}} \]

   if -1e133 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e94

   1. Initial program 83.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 83.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 83.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 80.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 80.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 80.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 80.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 81.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 81.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 81.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 89.3%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   6. Taylor expanded in x around 0 84.4%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} - 4 \cdot \frac{a \cdot t}{c} \]

   7. Taylor expanded in c around 0 84.0%

      \[\leadsto \color{blue}{\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}} \]

   if 1e94 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.99999999999999972e193

   1. Initial program 90.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 90.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 90.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 85.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 85.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 85.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 85.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 75.4%

      \[\leadsto \color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]
   6. Step-by-step derivation

      1. +-commutative 75.4%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right) + b}}{c \cdot z} \]

      2. *-commutative 75.4%

         \[\leadsto \frac{9 \cdot \left(x \cdot y\right) + b}{\color{blue}{z \cdot c}} \]

   7. Simplified 75.4%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right) + b}{z \cdot c}} \]

   if 4.99999999999999972e193 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 60.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 60.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 60.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 60.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 60.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 60.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 60.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 47.0%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 47.0%

         \[\leadsto \color{blue}{\frac{x \cdot y}{c \cdot z} \cdot 9} \]

      2. associate-/l* 56.8%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \cdot 9 \]

      3. associate-*l* 56.7%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right)} \]

      4. *-commutative 56.7%

         \[\leadsto x \cdot \color{blue}{\left(9 \cdot \frac{y}{c \cdot z}\right)} \]

      5. associate-*r/ 56.7%

         \[\leadsto x \cdot \color{blue}{\frac{9 \cdot y}{c \cdot z}} \]

      6. *-commutative 56.7%

         \[\leadsto x \cdot \frac{\color{blue}{y \cdot 9}}{c \cdot z} \]

      7. associate-/l* 56.7%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot \frac{9}{c \cdot z}\right)} \]

      8. *-commutative 56.7%

         \[\leadsto x \cdot \left(y \cdot \frac{9}{\color{blue}{z \cdot c}}\right) \]

   7. Simplified 56.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{9}{z \cdot c}\right)} \]

   8. Taylor expanded in y around 0 56.7%

      \[\leadsto x \cdot \color{blue}{\left(9 \cdot \frac{y}{c \cdot z}\right)} \]
   9. Step-by-step derivation

      1. associate-*r/ 56.7%

         \[\leadsto x \cdot \color{blue}{\frac{9 \cdot y}{c \cdot z}} \]

      2. *-commutative 56.7%

         \[\leadsto x \cdot \frac{\color{blue}{y \cdot 9}}{c \cdot z} \]

      3. times-frac 69.9%

         \[\leadsto x \cdot \color{blue}{\left(\frac{y}{c} \cdot \frac{9}{z}\right)} \]

      4. associate-*l/ 66.7%

         \[\leadsto x \cdot \color{blue}{\frac{y \cdot \frac{9}{z}}{c}} \]

   10. Simplified 66.7%

       \[\leadsto x \cdot \color{blue}{\frac{y \cdot \frac{9}{z}}{c}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(9 \cdot x\right) \leq -1 \cdot 10^{+133}:\\ \;\;\;\;x \cdot \frac{\frac{y}{c}}{\frac{z}{9}}\\ \mathbf{elif}\;y \cdot \left(9 \cdot x\right) \leq 10^{+94}:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;y \cdot \left(9 \cdot x\right) \leq 5 \cdot 10^{+193}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot \frac{9}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(9 \cdot x\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+97} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+95}\right):\\ \;\;\;\;\frac{9 \cdot \left(\frac{y}{z} \cdot x\right) - t \cdot \left(4 \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c} - 4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* 9.0 x))))
   (if (or (<= t_1 -5e+97) (not (<= t_1 2e+95)))
     (/ (- (* 9.0 (* (/ y z) x)) (* t (* 4.0 a))) c)
     (- (/ b (* z c)) (* 4.0 (/ (* a t) c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (9.0 * x);
	double tmp;
	if ((t_1 <= -5e+97) || !(t_1 <= 2e+95)) {
		tmp = ((9.0 * ((y / z) * x)) - (t * (4.0 * a))) / c;
	} else {
		tmp = (b / (z * c)) - (4.0 * ((a * t) / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (9.0d0 * x)
    if ((t_1 <= (-5d+97)) .or. (.not. (t_1 <= 2d+95))) then
        tmp = ((9.0d0 * ((y / z) * x)) - (t * (4.0d0 * a))) / c
    else
        tmp = (b / (z * c)) - (4.0d0 * ((a * t) / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (9.0 * x);
	double tmp;
	if ((t_1 <= -5e+97) || !(t_1 <= 2e+95)) {
		tmp = ((9.0 * ((y / z) * x)) - (t * (4.0 * a))) / c;
	} else {
		tmp = (b / (z * c)) - (4.0 * ((a * t) / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = y * (9.0 * x)
	tmp = 0
	if (t_1 <= -5e+97) or not (t_1 <= 2e+95):
		tmp = ((9.0 * ((y / z) * x)) - (t * (4.0 * a))) / c
	else:
		tmp = (b / (z * c)) - (4.0 * ((a * t) / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(9.0 * x))
	tmp = 0.0
	if ((t_1 <= -5e+97) || !(t_1 <= 2e+95))
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / z) * x)) - Float64(t * Float64(4.0 * a))) / c);
	else
		tmp = Float64(Float64(b / Float64(z * c)) - Float64(4.0 * Float64(Float64(a * t) / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = y * (9.0 * x);
	tmp = 0.0;
	if ((t_1 <= -5e+97) || ~((t_1 <= 2e+95)))
		tmp = ((9.0 * ((y / z) * x)) - (t * (4.0 * a))) / c;
	else
		tmp = (b / (z * c)) - (4.0 * ((a * t) / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+97], N[Not[LessEqual[t$95$1, 2e+95]], $MachinePrecision]], N[(N[(N[(9.0 * N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] - N[(t * N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.99999999999999999e97 or 2.00000000000000004e95 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 70.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 70.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 70.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 70.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 70.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 70.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 70.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 71.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 71.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 71.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 62.1%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   6. Taylor expanded in c around 0 69.1%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   7. Taylor expanded in b around 0 68.6%

      \[\leadsto \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} - 4 \cdot \left(a \cdot t\right)}{c}} \]
   8. Step-by-step derivation

      1. *-commutative 68.6%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot y}{z} \cdot 9} - 4 \cdot \left(a \cdot t\right)}{c} \]

      2. associate-*r/ 80.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot \frac{y}{z}\right)} \cdot 9 - 4 \cdot \left(a \cdot t\right)}{c} \]

      3. associate-*r* 80.2%

         \[\leadsto \frac{\left(x \cdot \frac{y}{z}\right) \cdot 9 - \color{blue}{\left(4 \cdot a\right) \cdot t}}{c} \]

      4. *-commutative 80.2%

         \[\leadsto \frac{\left(x \cdot \frac{y}{z}\right) \cdot 9 - \color{blue}{t \cdot \left(4 \cdot a\right)}}{c} \]

   9. Simplified 80.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \frac{y}{z}\right) \cdot 9 - t \cdot \left(4 \cdot a\right)}{c}} \]

   if -4.99999999999999999e97 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2.00000000000000004e95

   1. Initial program 83.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 83.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 83.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 80.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 80.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 80.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 80.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 82.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 82.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 82.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 89.6%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   6. Taylor expanded in x around 0 85.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} - 4 \cdot \frac{a \cdot t}{c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(9 \cdot x\right) \leq -5 \cdot 10^{+97} \lor \neg \left(y \cdot \left(9 \cdot x\right) \leq 2 \cdot 10^{+95}\right):\\ \;\;\;\;\frac{9 \cdot \left(\frac{y}{z} \cdot x\right) - t \cdot \left(4 \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c} - 4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(9 \cdot x\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+133}:\\ \;\;\;\;x \cdot \frac{\frac{y}{c}}{\frac{z}{9}}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+132}:\\ \;\;\;\;\frac{b}{z \cdot c} - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(9 \cdot \frac{x}{c} + \frac{b}{y \cdot c}\right)}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* 9.0 x))))
   (if (<= t_1 -1e+133)
     (* x (/ (/ y c) (/ z 9.0)))
     (if (<= t_1 2e+132)
       (- (/ b (* z c)) (* 4.0 (/ (* a t) c)))
       (/ (* y (+ (* 9.0 (/ x c)) (/ b (* y c)))) z)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (9.0 * x);
	double tmp;
	if (t_1 <= -1e+133) {
		tmp = x * ((y / c) / (z / 9.0));
	} else if (t_1 <= 2e+132) {
		tmp = (b / (z * c)) - (4.0 * ((a * t) / c));
	} else {
		tmp = (y * ((9.0 * (x / c)) + (b / (y * c)))) / z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (9.0d0 * x)
    if (t_1 <= (-1d+133)) then
        tmp = x * ((y / c) / (z / 9.0d0))
    else if (t_1 <= 2d+132) then
        tmp = (b / (z * c)) - (4.0d0 * ((a * t) / c))
    else
        tmp = (y * ((9.0d0 * (x / c)) + (b / (y * c)))) / z
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (9.0 * x);
	double tmp;
	if (t_1 <= -1e+133) {
		tmp = x * ((y / c) / (z / 9.0));
	} else if (t_1 <= 2e+132) {
		tmp = (b / (z * c)) - (4.0 * ((a * t) / c));
	} else {
		tmp = (y * ((9.0 * (x / c)) + (b / (y * c)))) / z;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = y * (9.0 * x)
	tmp = 0
	if t_1 <= -1e+133:
		tmp = x * ((y / c) / (z / 9.0))
	elif t_1 <= 2e+132:
		tmp = (b / (z * c)) - (4.0 * ((a * t) / c))
	else:
		tmp = (y * ((9.0 * (x / c)) + (b / (y * c)))) / z
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(9.0 * x))
	tmp = 0.0
	if (t_1 <= -1e+133)
		tmp = Float64(x * Float64(Float64(y / c) / Float64(z / 9.0)));
	elseif (t_1 <= 2e+132)
		tmp = Float64(Float64(b / Float64(z * c)) - Float64(4.0 * Float64(Float64(a * t) / c)));
	else
		tmp = Float64(Float64(y * Float64(Float64(9.0 * Float64(x / c)) + Float64(b / Float64(y * c)))) / z);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = y * (9.0 * x);
	tmp = 0.0;
	if (t_1 <= -1e+133)
		tmp = x * ((y / c) / (z / 9.0));
	elseif (t_1 <= 2e+132)
		tmp = (b / (z * c)) - (4.0 * ((a * t) / c));
	else
		tmp = (y * ((9.0 * (x / c)) + (b / (y * c)))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+133], N[(x * N[(N[(y / c), $MachinePrecision] / N[(z / 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+132], N[(N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(9.0 * N[(x / c), $MachinePrecision]), $MachinePrecision] + N[(b / N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e133

   1. Initial program 68.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 68.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 68.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 70.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 70.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 70.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 72.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 59.4%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 59.4%

         \[\leadsto \color{blue}{\frac{x \cdot y}{c \cdot z} \cdot 9} \]

      2. associate-/l* 72.7%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \cdot 9 \]

      3. associate-*l* 72.8%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right)} \]

      4. *-commutative 72.8%

         \[\leadsto x \cdot \color{blue}{\left(9 \cdot \frac{y}{c \cdot z}\right)} \]

      5. associate-*r/ 72.7%

         \[\leadsto x \cdot \color{blue}{\frac{9 \cdot y}{c \cdot z}} \]

      6. *-commutative 72.7%

         \[\leadsto x \cdot \frac{\color{blue}{y \cdot 9}}{c \cdot z} \]

      7. associate-/l* 72.6%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot \frac{9}{c \cdot z}\right)} \]

      8. *-commutative 72.6%

         \[\leadsto x \cdot \left(y \cdot \frac{9}{\color{blue}{z \cdot c}}\right) \]

   7. Simplified 72.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{9}{z \cdot c}\right)} \]
   8. Step-by-step derivation

      1. clear-num 72.6%

         \[\leadsto x \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{z \cdot c}{9}}}\right) \]

      2. inv-pow 72.6%

         \[\leadsto x \cdot \left(y \cdot \color{blue}{{\left(\frac{z \cdot c}{9}\right)}^{-1}}\right) \]

      3. *-commutative 72.6%

         \[\leadsto x \cdot \left(y \cdot {\left(\frac{\color{blue}{c \cdot z}}{9}\right)}^{-1}\right) \]

   9. Applied egg-rr 72.6%

      \[\leadsto x \cdot \left(y \cdot \color{blue}{{\left(\frac{c \cdot z}{9}\right)}^{-1}}\right) \]
   10. Step-by-step derivation

       1. unpow-1 72.6%

          \[\leadsto x \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{c \cdot z}{9}}}\right) \]

   11. Simplified 72.6%

       \[\leadsto x \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{c \cdot z}{9}}}\right) \]
   12. Step-by-step derivation

       1. pow1 72.6%

          \[\leadsto \color{blue}{{\left(x \cdot \left(y \cdot \frac{1}{\frac{c \cdot z}{9}}\right)\right)}^{1}} \]

       2. un-div-inv 72.8%

          \[\leadsto {\left(x \cdot \color{blue}{\frac{y}{\frac{c \cdot z}{9}}}\right)}^{1} \]

       3. associate-/l* 72.7%

          \[\leadsto {\left(x \cdot \frac{y}{\color{blue}{c \cdot \frac{z}{9}}}\right)}^{1} \]

   13. Applied egg-rr 72.7%

       \[\leadsto \color{blue}{{\left(x \cdot \frac{y}{c \cdot \frac{z}{9}}\right)}^{1}} \]
   14. Step-by-step derivation

       1. unpow1 72.7%

          \[\leadsto \color{blue}{x \cdot \frac{y}{c \cdot \frac{z}{9}}} \]

       2. associate-/r* 77.3%

          \[\leadsto x \cdot \color{blue}{\frac{\frac{y}{c}}{\frac{z}{9}}} \]

   15. Simplified 77.3%

       \[\leadsto \color{blue}{x \cdot \frac{\frac{y}{c}}{\frac{z}{9}}} \]

   if -1e133 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999998e132

   1. Initial program 84.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 84.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 84.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 81.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 81.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 81.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 81.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 83.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 83.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 83.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 89.3%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   6. Taylor expanded in x around 0 83.2%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} - 4 \cdot \frac{a \cdot t}{c} \]

   if 1.99999999999999998e132 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 65.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 65.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 65.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 65.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 65.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 65.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 65.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 65.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 65.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 65.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 74.1%

      \[\leadsto \color{blue}{y \cdot \left(\left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot y}\right)} \]

   6. Taylor expanded in z around 0 70.5%

      \[\leadsto \color{blue}{\frac{y \cdot \left(9 \cdot \frac{x}{c} + \frac{b}{c \cdot y}\right)}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(9 \cdot x\right) \leq -1 \cdot 10^{+133}:\\ \;\;\;\;x \cdot \frac{\frac{y}{c}}{\frac{z}{9}}\\ \mathbf{elif}\;y \cdot \left(9 \cdot x\right) \leq 2 \cdot 10^{+132}:\\ \;\;\;\;\frac{b}{z \cdot c} - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(9 \cdot \frac{x}{c} + \frac{b}{y \cdot c}\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{if}\;t \leq -8.8 \cdot 10^{+172}:\\ \;\;\;\;-4 \cdot \frac{1}{\frac{1}{a \cdot \frac{t}{c}}}\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+33}:\\ \;\;\;\;-4 \cdot \frac{1}{\frac{\frac{c}{t}}{a}}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-138}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-4}{\frac{c}{a}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (* 9.0 (* y x))) (* z c))))
   (if (<= t -8.8e+172)
     (* -4.0 (/ 1.0 (/ 1.0 (* a (/ t c)))))
     (if (<= t -3.3e+71)
       t_1
       (if (<= t -3.5e+33)
         (* -4.0 (/ 1.0 (/ (/ c t) a)))
         (if (<= t 2.2e-138) t_1 (* t (/ -4.0 (/ c a)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (9.0 * (y * x))) / (z * c);
	double tmp;
	if (t <= -8.8e+172) {
		tmp = -4.0 * (1.0 / (1.0 / (a * (t / c))));
	} else if (t <= -3.3e+71) {
		tmp = t_1;
	} else if (t <= -3.5e+33) {
		tmp = -4.0 * (1.0 / ((c / t) / a));
	} else if (t <= 2.2e-138) {
		tmp = t_1;
	} else {
		tmp = t * (-4.0 / (c / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b + (9.0d0 * (y * x))) / (z * c)
    if (t <= (-8.8d+172)) then
        tmp = (-4.0d0) * (1.0d0 / (1.0d0 / (a * (t / c))))
    else if (t <= (-3.3d+71)) then
        tmp = t_1
    else if (t <= (-3.5d+33)) then
        tmp = (-4.0d0) * (1.0d0 / ((c / t) / a))
    else if (t <= 2.2d-138) then
        tmp = t_1
    else
        tmp = t * ((-4.0d0) / (c / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (9.0 * (y * x))) / (z * c);
	double tmp;
	if (t <= -8.8e+172) {
		tmp = -4.0 * (1.0 / (1.0 / (a * (t / c))));
	} else if (t <= -3.3e+71) {
		tmp = t_1;
	} else if (t <= -3.5e+33) {
		tmp = -4.0 * (1.0 / ((c / t) / a));
	} else if (t <= 2.2e-138) {
		tmp = t_1;
	} else {
		tmp = t * (-4.0 / (c / a));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (b + (9.0 * (y * x))) / (z * c)
	tmp = 0
	if t <= -8.8e+172:
		tmp = -4.0 * (1.0 / (1.0 / (a * (t / c))))
	elif t <= -3.3e+71:
		tmp = t_1
	elif t <= -3.5e+33:
		tmp = -4.0 * (1.0 / ((c / t) / a))
	elif t <= 2.2e-138:
		tmp = t_1
	else:
		tmp = t * (-4.0 / (c / a))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c))
	tmp = 0.0
	if (t <= -8.8e+172)
		tmp = Float64(-4.0 * Float64(1.0 / Float64(1.0 / Float64(a * Float64(t / c)))));
	elseif (t <= -3.3e+71)
		tmp = t_1;
	elseif (t <= -3.5e+33)
		tmp = Float64(-4.0 * Float64(1.0 / Float64(Float64(c / t) / a)));
	elseif (t <= 2.2e-138)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(-4.0 / Float64(c / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b + (9.0 * (y * x))) / (z * c);
	tmp = 0.0;
	if (t <= -8.8e+172)
		tmp = -4.0 * (1.0 / (1.0 / (a * (t / c))));
	elseif (t <= -3.3e+71)
		tmp = t_1;
	elseif (t <= -3.5e+33)
		tmp = -4.0 * (1.0 / ((c / t) / a));
	elseif (t <= 2.2e-138)
		tmp = t_1;
	else
		tmp = t * (-4.0 / (c / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.8e+172], N[(-4.0 * N[(1.0 / N[(1.0 / N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.3e+71], t$95$1, If[LessEqual[t, -3.5e+33], N[(-4.0 * N[(1.0 / N[(N[(c / t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e-138], t$95$1, N[(t * N[(-4.0 / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.8000000000000005e172

   1. Initial program 66.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 66.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 66.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 72.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 72.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 72.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 76.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 67.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. clear-num 66.9%

         \[\leadsto -4 \cdot \color{blue}{\frac{1}{\frac{c}{a \cdot t}}} \]

      2. inv-pow 66.9%

         \[\leadsto -4 \cdot \color{blue}{{\left(\frac{c}{a \cdot t}\right)}^{-1}} \]

      3. *-commutative 66.9%

         \[\leadsto -4 \cdot {\left(\frac{c}{\color{blue}{t \cdot a}}\right)}^{-1} \]

   7. Applied egg-rr 66.9%

      \[\leadsto -4 \cdot \color{blue}{{\left(\frac{c}{t \cdot a}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 66.9%

         \[\leadsto -4 \cdot \color{blue}{\frac{1}{\frac{c}{t \cdot a}}} \]

      2. *-commutative 66.9%

         \[\leadsto -4 \cdot \frac{1}{\frac{c}{\color{blue}{a \cdot t}}} \]

   9. Simplified 66.9%

      \[\leadsto -4 \cdot \color{blue}{\frac{1}{\frac{c}{a \cdot t}}} \]
   10. Step-by-step derivation

       1. clear-num 67.0%

          \[\leadsto -4 \cdot \frac{1}{\color{blue}{\frac{1}{\frac{a \cdot t}{c}}}} \]

       2. associate-*r/ 79.3%

          \[\leadsto -4 \cdot \frac{1}{\frac{1}{\color{blue}{a \cdot \frac{t}{c}}}} \]

       3. inv-pow 79.3%

          \[\leadsto -4 \cdot \frac{1}{\color{blue}{{\left(a \cdot \frac{t}{c}\right)}^{-1}}} \]

   11. Applied egg-rr 79.3%

       \[\leadsto -4 \cdot \frac{1}{\color{blue}{{\left(a \cdot \frac{t}{c}\right)}^{-1}}} \]
   12. Step-by-step derivation

       1. unpow-1 79.3%

          \[\leadsto -4 \cdot \frac{1}{\color{blue}{\frac{1}{a \cdot \frac{t}{c}}}} \]

   13. Simplified 79.3%

       \[\leadsto -4 \cdot \frac{1}{\color{blue}{\frac{1}{a \cdot \frac{t}{c}}}} \]

   if -8.8000000000000005e172 < t < -3.2999999999999998e71 or -3.5000000000000001e33 < t < 2.1999999999999999e-138

   1. Initial program 84.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 84.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 84.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 80.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 80.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 80.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 80.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 66.4%

      \[\leadsto \color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]
   6. Step-by-step derivation

      1. +-commutative 66.4%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right) + b}}{c \cdot z} \]

      2. *-commutative 66.4%

         \[\leadsto \frac{9 \cdot \left(x \cdot y\right) + b}{\color{blue}{z \cdot c}} \]

   7. Simplified 66.4%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right) + b}{z \cdot c}} \]

   if -3.2999999999999998e71 < t < -3.5000000000000001e33

   1. Initial program 68.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 68.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 68.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 68.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 68.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 68.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 68.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 45.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. clear-num 45.6%

         \[\leadsto -4 \cdot \color{blue}{\frac{1}{\frac{c}{a \cdot t}}} \]

      2. inv-pow 45.6%

         \[\leadsto -4 \cdot \color{blue}{{\left(\frac{c}{a \cdot t}\right)}^{-1}} \]

      3. *-commutative 45.6%

         \[\leadsto -4 \cdot {\left(\frac{c}{\color{blue}{t \cdot a}}\right)}^{-1} \]

   7. Applied egg-rr 45.6%

      \[\leadsto -4 \cdot \color{blue}{{\left(\frac{c}{t \cdot a}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 45.6%

         \[\leadsto -4 \cdot \color{blue}{\frac{1}{\frac{c}{t \cdot a}}} \]

      2. associate-/r* 56.3%

         \[\leadsto -4 \cdot \frac{1}{\color{blue}{\frac{\frac{c}{t}}{a}}} \]

   9. Simplified 56.3%

      \[\leadsto -4 \cdot \color{blue}{\frac{1}{\frac{\frac{c}{t}}{a}}} \]

   if 2.1999999999999999e-138 < t

   1. Initial program 74.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 74.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 74.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 74.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 74.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 74.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 74.2%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 49.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. clear-num 49.2%

         \[\leadsto -4 \cdot \color{blue}{\frac{1}{\frac{c}{a \cdot t}}} \]

      2. inv-pow 49.2%

         \[\leadsto -4 \cdot \color{blue}{{\left(\frac{c}{a \cdot t}\right)}^{-1}} \]

      3. *-commutative 49.2%

         \[\leadsto -4 \cdot {\left(\frac{c}{\color{blue}{t \cdot a}}\right)}^{-1} \]

   7. Applied egg-rr 49.2%

      \[\leadsto -4 \cdot \color{blue}{{\left(\frac{c}{t \cdot a}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 49.2%

         \[\leadsto -4 \cdot \color{blue}{\frac{1}{\frac{c}{t \cdot a}}} \]

      2. *-commutative 49.2%

         \[\leadsto -4 \cdot \frac{1}{\frac{c}{\color{blue}{a \cdot t}}} \]

   9. Simplified 49.2%

      \[\leadsto -4 \cdot \color{blue}{\frac{1}{\frac{c}{a \cdot t}}} \]
   10. Step-by-step derivation

       1. un-div-inv 49.2%

          \[\leadsto \color{blue}{\frac{-4}{\frac{c}{a \cdot t}}} \]

       2. associate-/r* 51.3%

          \[\leadsto \frac{-4}{\color{blue}{\frac{\frac{c}{a}}{t}}} \]

   11. Applied egg-rr 51.3%

       \[\leadsto \color{blue}{\frac{-4}{\frac{\frac{c}{a}}{t}}} \]
   12. Step-by-step derivation

       1. associate-/r/ 51.4%

          \[\leadsto \color{blue}{\frac{-4}{\frac{c}{a}} \cdot t} \]

   13. Simplified 51.4%

       \[\leadsto \color{blue}{\frac{-4}{\frac{c}{a}} \cdot t} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+172}:\\ \;\;\;\;-4 \cdot \frac{1}{\frac{1}{a \cdot \frac{t}{c}}}\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{+71}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+33}:\\ \;\;\;\;-4 \cdot \frac{1}{\frac{\frac{c}{t}}{a}}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-138}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-4}{\frac{c}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 92.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-16} \lor \neg \left(z \leq 2.5 \cdot 10^{-71}\right):\\ \;\;\;\;\frac{\left(\frac{b}{z} + 9 \cdot \left(\frac{y}{z} \cdot x\right)\right) - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + t \cdot \left(9 \cdot \frac{y \cdot x}{t} - 4 \cdot \left(z \cdot a\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -7.5e-16) (not (<= z 2.5e-71)))
   (/ (- (+ (/ b z) (* 9.0 (* (/ y z) x))) (* 4.0 (* a t))) c)
   (/ (+ b (* t (- (* 9.0 (/ (* y x) t)) (* 4.0 (* z a))))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -7.5e-16) || !(z <= 2.5e-71)) {
		tmp = (((b / z) + (9.0 * ((y / z) * x))) - (4.0 * (a * t))) / c;
	} else {
		tmp = (b + (t * ((9.0 * ((y * x) / t)) - (4.0 * (z * a))))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-7.5d-16)) .or. (.not. (z <= 2.5d-71))) then
        tmp = (((b / z) + (9.0d0 * ((y / z) * x))) - (4.0d0 * (a * t))) / c
    else
        tmp = (b + (t * ((9.0d0 * ((y * x) / t)) - (4.0d0 * (z * a))))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -7.5e-16) || !(z <= 2.5e-71)) {
		tmp = (((b / z) + (9.0 * ((y / z) * x))) - (4.0 * (a * t))) / c;
	} else {
		tmp = (b + (t * ((9.0 * ((y * x) / t)) - (4.0 * (z * a))))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -7.5e-16) or not (z <= 2.5e-71):
		tmp = (((b / z) + (9.0 * ((y / z) * x))) - (4.0 * (a * t))) / c
	else:
		tmp = (b + (t * ((9.0 * ((y * x) / t)) - (4.0 * (z * a))))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -7.5e-16) || !(z <= 2.5e-71))
		tmp = Float64(Float64(Float64(Float64(b / z) + Float64(9.0 * Float64(Float64(y / z) * x))) - Float64(4.0 * Float64(a * t))) / c);
	else
		tmp = Float64(Float64(b + Float64(t * Float64(Float64(9.0 * Float64(Float64(y * x) / t)) - Float64(4.0 * Float64(z * a))))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -7.5e-16) || ~((z <= 2.5e-71)))
		tmp = (((b / z) + (9.0 * ((y / z) * x))) - (4.0 * (a * t))) / c;
	else
		tmp = (b + (t * ((9.0 * ((y * x) / t)) - (4.0 * (z * a))))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -7.5e-16], N[Not[LessEqual[z, 2.5e-71]], $MachinePrecision]], N[(N[(N[(N[(b / z), $MachinePrecision] + N[(9.0 * N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(t * N[(N[(9.0 * N[(N[(y * x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5e-16 or 2.49999999999999999e-71 < z

   1. Initial program 68.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 68.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 68.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 65.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 65.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 65.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 65.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 70.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 70.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 70.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 81.2%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   6. Taylor expanded in c around 0 88.8%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]
   7. Step-by-step derivation

      1. associate-*r/ 95.9%

         \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(x \cdot \frac{y}{z}\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

      2. *-commutative 95.9%

         \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

   8. Applied egg-rr 95.9%

      \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

   if -7.5e-16 < z < 2.49999999999999999e-71

   1. Initial program 93.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 93.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 93.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 94.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 94.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 94.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 94.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 89.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 89.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 91.3%

      \[\leadsto \frac{\color{blue}{t \cdot \left(9 \cdot \frac{x \cdot y}{t} - 4 \cdot \left(a \cdot z\right)\right)} + b}{z \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-16} \lor \neg \left(z \leq 2.5 \cdot 10^{-71}\right):\\ \;\;\;\;\frac{\left(\frac{b}{z} + 9 \cdot \left(\frac{y}{z} \cdot x\right)\right) - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + t \cdot \left(9 \cdot \frac{y \cdot x}{t} - 4 \cdot \left(z \cdot a\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 75.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(9 \cdot x\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+133}:\\ \;\;\;\;x \cdot \frac{\frac{y}{c}}{\frac{z}{9}}\\ \mathbf{elif}\;t\_1 \leq 10^{+147}:\\ \;\;\;\;\frac{b}{z \cdot c} - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot \frac{9}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* 9.0 x))))
   (if (<= t_1 -1e+133)
     (* x (/ (/ y c) (/ z 9.0)))
     (if (<= t_1 1e+147)
       (- (/ b (* z c)) (* 4.0 (/ (* a t) c)))
       (* x (/ (* y (/ 9.0 z)) c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (9.0 * x);
	double tmp;
	if (t_1 <= -1e+133) {
		tmp = x * ((y / c) / (z / 9.0));
	} else if (t_1 <= 1e+147) {
		tmp = (b / (z * c)) - (4.0 * ((a * t) / c));
	} else {
		tmp = x * ((y * (9.0 / z)) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (9.0d0 * x)
    if (t_1 <= (-1d+133)) then
        tmp = x * ((y / c) / (z / 9.0d0))
    else if (t_1 <= 1d+147) then
        tmp = (b / (z * c)) - (4.0d0 * ((a * t) / c))
    else
        tmp = x * ((y * (9.0d0 / z)) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (9.0 * x);
	double tmp;
	if (t_1 <= -1e+133) {
		tmp = x * ((y / c) / (z / 9.0));
	} else if (t_1 <= 1e+147) {
		tmp = (b / (z * c)) - (4.0 * ((a * t) / c));
	} else {
		tmp = x * ((y * (9.0 / z)) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = y * (9.0 * x)
	tmp = 0
	if t_1 <= -1e+133:
		tmp = x * ((y / c) / (z / 9.0))
	elif t_1 <= 1e+147:
		tmp = (b / (z * c)) - (4.0 * ((a * t) / c))
	else:
		tmp = x * ((y * (9.0 / z)) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(9.0 * x))
	tmp = 0.0
	if (t_1 <= -1e+133)
		tmp = Float64(x * Float64(Float64(y / c) / Float64(z / 9.0)));
	elseif (t_1 <= 1e+147)
		tmp = Float64(Float64(b / Float64(z * c)) - Float64(4.0 * Float64(Float64(a * t) / c)));
	else
		tmp = Float64(x * Float64(Float64(y * Float64(9.0 / z)) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = y * (9.0 * x);
	tmp = 0.0;
	if (t_1 <= -1e+133)
		tmp = x * ((y / c) / (z / 9.0));
	elseif (t_1 <= 1e+147)
		tmp = (b / (z * c)) - (4.0 * ((a * t) / c));
	else
		tmp = x * ((y * (9.0 / z)) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+133], N[(x * N[(N[(y / c), $MachinePrecision] / N[(z / 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+147], N[(N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * N[(9.0 / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e133

   1. Initial program 68.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 68.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 68.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 70.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 70.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 70.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 72.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 59.4%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 59.4%

         \[\leadsto \color{blue}{\frac{x \cdot y}{c \cdot z} \cdot 9} \]

      2. associate-/l* 72.7%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \cdot 9 \]

      3. associate-*l* 72.8%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right)} \]

      4. *-commutative 72.8%

         \[\leadsto x \cdot \color{blue}{\left(9 \cdot \frac{y}{c \cdot z}\right)} \]

      5. associate-*r/ 72.7%

         \[\leadsto x \cdot \color{blue}{\frac{9 \cdot y}{c \cdot z}} \]

      6. *-commutative 72.7%

         \[\leadsto x \cdot \frac{\color{blue}{y \cdot 9}}{c \cdot z} \]

      7. associate-/l* 72.6%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot \frac{9}{c \cdot z}\right)} \]

      8. *-commutative 72.6%

         \[\leadsto x \cdot \left(y \cdot \frac{9}{\color{blue}{z \cdot c}}\right) \]

   7. Simplified 72.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{9}{z \cdot c}\right)} \]
   8. Step-by-step derivation

      1. clear-num 72.6%

         \[\leadsto x \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{z \cdot c}{9}}}\right) \]

      2. inv-pow 72.6%

         \[\leadsto x \cdot \left(y \cdot \color{blue}{{\left(\frac{z \cdot c}{9}\right)}^{-1}}\right) \]

      3. *-commutative 72.6%

         \[\leadsto x \cdot \left(y \cdot {\left(\frac{\color{blue}{c \cdot z}}{9}\right)}^{-1}\right) \]

   9. Applied egg-rr 72.6%

      \[\leadsto x \cdot \left(y \cdot \color{blue}{{\left(\frac{c \cdot z}{9}\right)}^{-1}}\right) \]
   10. Step-by-step derivation

       1. unpow-1 72.6%

          \[\leadsto x \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{c \cdot z}{9}}}\right) \]

   11. Simplified 72.6%

       \[\leadsto x \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{c \cdot z}{9}}}\right) \]
   12. Step-by-step derivation

       1. pow1 72.6%

          \[\leadsto \color{blue}{{\left(x \cdot \left(y \cdot \frac{1}{\frac{c \cdot z}{9}}\right)\right)}^{1}} \]

       2. un-div-inv 72.8%

          \[\leadsto {\left(x \cdot \color{blue}{\frac{y}{\frac{c \cdot z}{9}}}\right)}^{1} \]

       3. associate-/l* 72.7%

          \[\leadsto {\left(x \cdot \frac{y}{\color{blue}{c \cdot \frac{z}{9}}}\right)}^{1} \]

   13. Applied egg-rr 72.7%

       \[\leadsto \color{blue}{{\left(x \cdot \frac{y}{c \cdot \frac{z}{9}}\right)}^{1}} \]
   14. Step-by-step derivation

       1. unpow1 72.7%

          \[\leadsto \color{blue}{x \cdot \frac{y}{c \cdot \frac{z}{9}}} \]

       2. associate-/r* 77.3%

          \[\leadsto x \cdot \color{blue}{\frac{\frac{y}{c}}{\frac{z}{9}}} \]

   15. Simplified 77.3%

       \[\leadsto \color{blue}{x \cdot \frac{\frac{y}{c}}{\frac{z}{9}}} \]

   if -1e133 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.9999999999999998e146

   1. Initial program 84.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 84.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 84.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 81.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 81.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 81.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 81.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 83.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 83.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 83.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 89.5%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   6. Taylor expanded in x around 0 82.5%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} - 4 \cdot \frac{a \cdot t}{c} \]

   if 9.9999999999999998e146 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 61.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 61.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 61.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 61.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 61.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 61.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 61.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 50.6%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 50.6%

         \[\leadsto \color{blue}{\frac{x \cdot y}{c \cdot z} \cdot 9} \]

      2. associate-/l* 58.7%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \cdot 9 \]

      3. associate-*l* 58.6%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right)} \]

      4. *-commutative 58.6%

         \[\leadsto x \cdot \color{blue}{\left(9 \cdot \frac{y}{c \cdot z}\right)} \]

      5. associate-*r/ 58.6%

         \[\leadsto x \cdot \color{blue}{\frac{9 \cdot y}{c \cdot z}} \]

      6. *-commutative 58.6%

         \[\leadsto x \cdot \frac{\color{blue}{y \cdot 9}}{c \cdot z} \]

      7. associate-/l* 58.6%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot \frac{9}{c \cdot z}\right)} \]

      8. *-commutative 58.6%

         \[\leadsto x \cdot \left(y \cdot \frac{9}{\color{blue}{z \cdot c}}\right) \]

   7. Simplified 58.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{9}{z \cdot c}\right)} \]

   8. Taylor expanded in y around 0 58.6%

      \[\leadsto x \cdot \color{blue}{\left(9 \cdot \frac{y}{c \cdot z}\right)} \]
   9. Step-by-step derivation

      1. associate-*r/ 58.6%

         \[\leadsto x \cdot \color{blue}{\frac{9 \cdot y}{c \cdot z}} \]

      2. *-commutative 58.6%

         \[\leadsto x \cdot \frac{\color{blue}{y \cdot 9}}{c \cdot z} \]

      3. times-frac 69.6%

         \[\leadsto x \cdot \color{blue}{\left(\frac{y}{c} \cdot \frac{9}{z}\right)} \]

      4. associate-*l/ 66.9%

         \[\leadsto x \cdot \color{blue}{\frac{y \cdot \frac{9}{z}}{c}} \]

   10. Simplified 66.9%

       \[\leadsto x \cdot \color{blue}{\frac{y \cdot \frac{9}{z}}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(9 \cdot x\right) \leq -1 \cdot 10^{+133}:\\ \;\;\;\;x \cdot \frac{\frac{y}{c}}{\frac{z}{9}}\\ \mathbf{elif}\;y \cdot \left(9 \cdot x\right) \leq 10^{+147}:\\ \;\;\;\;\frac{b}{z \cdot c} - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot \frac{9}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 94.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-35} \lor \neg \left(z \leq 4.4 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{\left(\frac{b}{z} + 9 \cdot \left(\frac{y}{z} \cdot x\right)\right) - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.8e-35) (not (<= z 4.4e-35)))
   (/ (- (+ (/ b z) (* 9.0 (* (/ y z) x))) (* 4.0 (* a t))) c)
   (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.8e-35) || !(z <= 4.4e-35)) {
		tmp = (((b / z) + (9.0 * ((y / z) * x))) - (4.0 * (a * t))) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-1.8d-35)) .or. (.not. (z <= 4.4d-35))) then
        tmp = (((b / z) + (9.0d0 * ((y / z) * x))) - (4.0d0 * (a * t))) / c
    else
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.8e-35) || !(z <= 4.4e-35)) {
		tmp = (((b / z) + (9.0 * ((y / z) * x))) - (4.0 * (a * t))) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -1.8e-35) or not (z <= 4.4e-35):
		tmp = (((b / z) + (9.0 * ((y / z) * x))) - (4.0 * (a * t))) / c
	else:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.8e-35) || !(z <= 4.4e-35))
		tmp = Float64(Float64(Float64(Float64(b / z) + Float64(9.0 * Float64(Float64(y / z) * x))) - Float64(4.0 * Float64(a * t))) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -1.8e-35) || ~((z <= 4.4e-35)))
		tmp = (((b / z) + (9.0 * ((y / z) * x))) - (4.0 * (a * t))) / c;
	else
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.8e-35], N[Not[LessEqual[z, 4.4e-35]], $MachinePrecision]], N[(N[(N[(N[(b / z), $MachinePrecision] + N[(9.0 * N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.80000000000000009e-35 or 4.39999999999999987e-35 < z

   1. Initial program 66.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 66.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 66.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 63.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 63.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 63.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 63.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 68.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 68.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 68.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 79.7%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   6. Taylor expanded in c around 0 87.4%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]
   7. Step-by-step derivation

      1. associate-*r/ 94.7%

         \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(x \cdot \frac{y}{z}\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

      2. *-commutative 94.7%

         \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

   8. Applied egg-rr 94.7%

      \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

   if -1.80000000000000009e-35 < z < 4.39999999999999987e-35

   1. Initial program 95.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-35} \lor \neg \left(z \leq 4.4 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{\left(\frac{b}{z} + 9 \cdot \left(\frac{y}{z} \cdot x\right)\right) - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 86.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+127} \lor \neg \left(z \leq 4.4 \cdot 10^{+153}\right):\\ \;\;\;\;\frac{9 \cdot \left(\frac{y}{z} \cdot x\right) - t \cdot \left(4 \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -2.5e+127) (not (<= z 4.4e+153)))
   (/ (- (* 9.0 (* (/ y z) x)) (* t (* 4.0 a))) c)
   (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2.5e+127) || !(z <= 4.4e+153)) {
		tmp = ((9.0 * ((y / z) * x)) - (t * (4.0 * a))) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-2.5d+127)) .or. (.not. (z <= 4.4d+153))) then
        tmp = ((9.0d0 * ((y / z) * x)) - (t * (4.0d0 * a))) / c
    else
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2.5e+127) || !(z <= 4.4e+153)) {
		tmp = ((9.0 * ((y / z) * x)) - (t * (4.0 * a))) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -2.5e+127) or not (z <= 4.4e+153):
		tmp = ((9.0 * ((y / z) * x)) - (t * (4.0 * a))) / c
	else:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -2.5e+127) || !(z <= 4.4e+153))
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / z) * x)) - Float64(t * Float64(4.0 * a))) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -2.5e+127) || ~((z <= 4.4e+153)))
		tmp = ((9.0 * ((y / z) * x)) - (t * (4.0 * a))) / c;
	else
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -2.5e+127], N[Not[LessEqual[z, 4.4e+153]], $MachinePrecision]], N[(N[(N[(9.0 * N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] - N[(t * N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5000000000000002e127 or 4.3999999999999999e153 < z

   1. Initial program 49.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 49.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 49.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 44.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 44.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 44.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 44.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 51.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 51.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 51.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 75.7%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   6. Taylor expanded in c around 0 85.5%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   7. Taylor expanded in b around 0 70.0%

      \[\leadsto \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} - 4 \cdot \left(a \cdot t\right)}{c}} \]
   8. Step-by-step derivation

      1. *-commutative 70.0%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot y}{z} \cdot 9} - 4 \cdot \left(a \cdot t\right)}{c} \]

      2. associate-*r/ 82.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot \frac{y}{z}\right)} \cdot 9 - 4 \cdot \left(a \cdot t\right)}{c} \]

      3. associate-*r* 82.5%

         \[\leadsto \frac{\left(x \cdot \frac{y}{z}\right) \cdot 9 - \color{blue}{\left(4 \cdot a\right) \cdot t}}{c} \]

      4. *-commutative 82.5%

         \[\leadsto \frac{\left(x \cdot \frac{y}{z}\right) \cdot 9 - \color{blue}{t \cdot \left(4 \cdot a\right)}}{c} \]

   9. Simplified 82.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \frac{y}{z}\right) \cdot 9 - t \cdot \left(4 \cdot a\right)}{c}} \]

   if -2.5000000000000002e127 < z < 4.3999999999999999e153

   1. Initial program 91.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+127} \lor \neg \left(z \leq 4.4 \cdot 10^{+153}\right):\\ \;\;\;\;\frac{9 \cdot \left(\frac{y}{z} \cdot x\right) - t \cdot \left(4 \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 85.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+130} \lor \neg \left(z \leq 1.8 \cdot 10^{+154}\right):\\ \;\;\;\;\frac{9 \cdot \left(\frac{y}{z} \cdot x\right) - t \cdot \left(4 \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.65e+130) (not (<= z 1.8e+154)))
   (/ (- (* 9.0 (* (/ y z) x)) (* t (* 4.0 a))) c)
   (/ (+ b (- (* x (* 9.0 y)) (* (* a t) (* z 4.0)))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.65e+130) || !(z <= 1.8e+154)) {
		tmp = ((9.0 * ((y / z) * x)) - (t * (4.0 * a))) / c;
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-1.65d+130)) .or. (.not. (z <= 1.8d+154))) then
        tmp = ((9.0d0 * ((y / z) * x)) - (t * (4.0d0 * a))) / c
    else
        tmp = (b + ((x * (9.0d0 * y)) - ((a * t) * (z * 4.0d0)))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.65e+130) || !(z <= 1.8e+154)) {
		tmp = ((9.0 * ((y / z) * x)) - (t * (4.0 * a))) / c;
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -1.65e+130) or not (z <= 1.8e+154):
		tmp = ((9.0 * ((y / z) * x)) - (t * (4.0 * a))) / c
	else:
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.65e+130) || !(z <= 1.8e+154))
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / z) * x)) - Float64(t * Float64(4.0 * a))) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(a * t) * Float64(z * 4.0)))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -1.65e+130) || ~((z <= 1.8e+154)))
		tmp = ((9.0 * ((y / z) * x)) - (t * (4.0 * a))) / c;
	else
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.65e+130], N[Not[LessEqual[z, 1.8e+154]], $MachinePrecision]], N[(N[(N[(9.0 * N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] - N[(t * N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65e130 or 1.8e154 < z

   1. Initial program 49.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 49.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 49.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 44.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 44.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 44.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 44.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 51.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 51.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 51.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 75.7%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   6. Taylor expanded in c around 0 85.5%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   7. Taylor expanded in b around 0 70.0%

      \[\leadsto \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} - 4 \cdot \left(a \cdot t\right)}{c}} \]
   8. Step-by-step derivation

      1. *-commutative 70.0%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot y}{z} \cdot 9} - 4 \cdot \left(a \cdot t\right)}{c} \]

      2. associate-*r/ 82.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot \frac{y}{z}\right)} \cdot 9 - 4 \cdot \left(a \cdot t\right)}{c} \]

      3. associate-*r* 82.5%

         \[\leadsto \frac{\left(x \cdot \frac{y}{z}\right) \cdot 9 - \color{blue}{\left(4 \cdot a\right) \cdot t}}{c} \]

      4. *-commutative 82.5%

         \[\leadsto \frac{\left(x \cdot \frac{y}{z}\right) \cdot 9 - \color{blue}{t \cdot \left(4 \cdot a\right)}}{c} \]

   9. Simplified 82.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \frac{y}{z}\right) \cdot 9 - t \cdot \left(4 \cdot a\right)}{c}} \]

   if -1.65e130 < z < 1.8e154

   1. Initial program 91.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 91.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 91.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 91.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 91.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 91.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 91.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 89.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 89.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 89.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+130} \lor \neg \left(z \leq 1.8 \cdot 10^{+154}\right):\\ \;\;\;\;\frac{9 \cdot \left(\frac{y}{z} \cdot x\right) - t \cdot \left(4 \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+143} \lor \neg \left(b \leq 2.9 \cdot 10^{+153}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -1.5e+143) (not (<= b 2.9e+153)))
   (/ (/ b c) z)
   (* a (/ (* t -4.0) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1.5e+143) || !(b <= 2.9e+153)) {
		tmp = (b / c) / z;
	} else {
		tmp = a * ((t * -4.0) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-1.5d+143)) .or. (.not. (b <= 2.9d+153))) then
        tmp = (b / c) / z
    else
        tmp = a * ((t * (-4.0d0)) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1.5e+143) || !(b <= 2.9e+153)) {
		tmp = (b / c) / z;
	} else {
		tmp = a * ((t * -4.0) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -1.5e+143) or not (b <= 2.9e+153):
		tmp = (b / c) / z
	else:
		tmp = a * ((t * -4.0) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -1.5e+143) || !(b <= 2.9e+153))
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(a * Float64(Float64(t * -4.0) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -1.5e+143) || ~((b <= 2.9e+153)))
		tmp = (b / c) / z;
	else
		tmp = a * ((t * -4.0) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -1.5e+143], N[Not[LessEqual[b, 2.9e+153]], $MachinePrecision]], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.5e143 or 2.90000000000000002e153 < b

   1. Initial program 81.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 81.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 81.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 83.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 83.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 83.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 83.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 80.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 80.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 80.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 73.0%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   6. Taylor expanded in c around 0 70.5%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]
   7. Step-by-step derivation

      1. associate-*r/ 74.5%

         \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(x \cdot \frac{y}{z}\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

      2. *-commutative 74.5%

         \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

   8. Applied egg-rr 74.5%

      \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

   9. Taylor expanded in b around inf 63.5%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   10. Step-by-step derivation

       1. associate-/r* 69.5%

          \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   11. Simplified 69.5%

       \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   if -1.5e143 < b < 2.90000000000000002e153

   1. Initial program 76.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 76.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 76.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 74.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 74.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 74.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 75.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 49.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 49.0%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 49.5%

         \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right)} \cdot -4 \]

      3. associate-*r* 49.5%

         \[\leadsto \color{blue}{a \cdot \left(\frac{t}{c} \cdot -4\right)} \]

      4. *-commutative 49.5%

         \[\leadsto a \cdot \color{blue}{\left(-4 \cdot \frac{t}{c}\right)} \]

      5. *-commutative 49.5%

         \[\leadsto a \cdot \color{blue}{\left(\frac{t}{c} \cdot -4\right)} \]

      6. associate-*l/ 49.5%

         \[\leadsto a \cdot \color{blue}{\frac{t \cdot -4}{c}} \]

   7. Simplified 49.5%

      \[\leadsto \color{blue}{a \cdot \frac{t \cdot -4}{c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+143} \lor \neg \left(b \leq 2.9 \cdot 10^{+153}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 48.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+144} \lor \neg \left(b \leq 4.9 \cdot 10^{+151}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -5e+144) (not (<= b 4.9e+151)))
   (/ (/ b c) z)
   (* -4.0 (/ (* a t) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -5e+144) || !(b <= 4.9e+151)) {
		tmp = (b / c) / z;
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-5d+144)) .or. (.not. (b <= 4.9d+151))) then
        tmp = (b / c) / z
    else
        tmp = (-4.0d0) * ((a * t) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -5e+144) || !(b <= 4.9e+151)) {
		tmp = (b / c) / z;
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -5e+144) or not (b <= 4.9e+151):
		tmp = (b / c) / z
	else:
		tmp = -4.0 * ((a * t) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -5e+144) || !(b <= 4.9e+151))
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -5e+144) || ~((b <= 4.9e+151)))
		tmp = (b / c) / z;
	else
		tmp = -4.0 * ((a * t) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -5e+144], N[Not[LessEqual[b, 4.9e+151]], $MachinePrecision]], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.9999999999999999e144 or 4.8999999999999999e151 < b

   1. Initial program 81.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 81.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 81.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 83.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 83.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 83.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 83.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 80.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 80.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 80.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 73.0%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   6. Taylor expanded in c around 0 70.5%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]
   7. Step-by-step derivation

      1. associate-*r/ 74.5%

         \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(x \cdot \frac{y}{z}\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

      2. *-commutative 74.5%

         \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

   8. Applied egg-rr 74.5%

      \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

   9. Taylor expanded in b around inf 63.5%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   10. Step-by-step derivation

       1. associate-/r* 69.5%

          \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   11. Simplified 69.5%

       \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   if -4.9999999999999999e144 < b < 4.8999999999999999e151

   1. Initial program 76.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 76.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 76.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 74.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 74.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 74.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 75.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 49.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+144} \lor \neg \left(b \leq 4.9 \cdot 10^{+151}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 35.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq 8.6 \cdot 10^{-253}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c 8.6e-253) (/ b (* z c)) (/ (/ b c) z)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 8.6e-253) {
		tmp = b / (z * c);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (c <= 8.6d-253) then
        tmp = b / (z * c)
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 8.6e-253) {
		tmp = b / (z * c);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= 8.6e-253:
		tmp = b / (z * c)
	else:
		tmp = (b / c) / z
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= 8.6e-253)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= 8.6e-253)
		tmp = b / (z * c);
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, 8.6e-253], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 8.6000000000000003e-253

   1. Initial program 81.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 81.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 81.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 79.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 38.5%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 38.5%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 38.5%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if 8.6000000000000003e-253 < c

   1. Initial program 74.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 74.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 74.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 74.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 74.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 74.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 74.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 74.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 74.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 74.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 75.6%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   6. Taylor expanded in c around 0 78.3%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]
   7. Step-by-step derivation

      1. associate-*r/ 82.0%

         \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(x \cdot \frac{y}{z}\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

      2. *-commutative 82.0%

         \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

   8. Applied egg-rr 82.0%

      \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(\frac{y}{z} \cdot x\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

   9. Taylor expanded in b around inf 24.8%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   10. Step-by-step derivation

       1. associate-/r* 29.8%

          \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   11. Simplified 29.8%

       \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 35.6% accurate, 3.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ b (* z c)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = b / (z * c)
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	return b / (z * c)

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(z * c))
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (z * c);
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.2%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 78.2%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. *-commutative 78.2%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

   3. associate-*r* 76.8%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

   4. *-commutative 76.8%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

   5. associate-+l- 76.8%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

3. Simplified 77.2%

   \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 32.3%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Step-by-step derivation

   1. *-commutative 32.3%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

7. Simplified 32.3%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
8. Add Preprocessing

Developer Target 1: 80.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t\_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t\_4}{z \cdot c}\\ t_6 := \frac{\left(t\_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 0:\\ \;\;\;\;\frac{\frac{t\_4}{z}}{c}\\ \mathbf{elif}\;t\_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t\_1\right) - t\_2\\ \mathbf{elif}\;t\_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024193 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) -220031348160821/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 0) (/ (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 365902434742109/31250000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 28768236795461370000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ (* (* 9 (/ y c)) (/ x z)) (/ b (* c z))) (* 4 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 138385150424563190000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (- (+ (* 9 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4 (/ (* a t) c)))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))